## 1 Introduction
[12] studied the deformation and damage characteristics of red sandstone at low temperatures by combining the effects of the rock strength properties, fractal dimension, and dissipated energy with microfracture morphology; they concluded that low temperatures led to a rapid loss of bearing capacity and a sharp decrease in the strength of the red sandstone under high-strain-rate loading, the dissipation energy of the frozen rock specimens was positively correlated with the fractal dimension, and the low-temperature effect produced significant cracks at the material interface of the red sandstone. [PERSON] et al. [13] used a method that employed a combination of low-field nuclear magnetic resonance (LF-NMR) and scanning electron microscopy (SEM) to investigate the dynamic evolution of the microstructure of frozen sandstones as a function of saturation and determine the increase in saturation; the elastic modulus showed a trend of increasing and then decreasing, and the ultimate deformation capacity showed the opposite trend. [PERSON] et al. [14] compared the uniaxial compression of sandstone, marble, and granite at different temperatures for different materials; the peak inflection point of the stress-strain curve was at \(-5\)\({}^{\circ}\)C, while the second inflection point temperature increased with the material hardness. [PERSON] et al. [15] conducted SHPB impact tests on frozen red sandstone specimens at \(-15\)\({}^{\circ}\)C, compared them with the static uniaxial compression tests, and found that the failure form was closely correlated to the average strain rate. The presence of water in the interior of coal and rock has also received widespread attention. [PERSON] et al. [16; 17] analysed the fracture of rocks under water-force coupling by means of experiments and simulations, on the basis of which a two-medium model was proposed. Regarding the effects of saturation and temperature on the wave speed of the corresponding ultrasonic wave, previous studies reached different conclusions. Generally, with increasing saturation, the internal gap of the sample is filled with a large number of water molecules, and the propagation of the ultrasonic waves in the water molecules is greater than that in air; thus, the wave speed of the sample significantly increases [18]. Moreover, as water saturation increases, the squeezing of internal moisture leads to a reduction in the internal strength and modulus of elasticity, ultimately leading to a reduction in the rate of wave propagation [19]. [PERSON] et al. [20] found that the stress in sandstone had a trend of increasing and then decreasing with decreasing temperature. With the decrease in temperature, the stress initially increased, then decreased and finally increased, similar to an \"N\" shape. [PERSON] et al. [21] concluded that the peak strength of water-saturated granite with decreasing temperature initially remained unchanged, then rapidly decreased and eventually converged to a stable value, similar to a \"\(\backslash\)\" shape. Based on the above literature, studies of temperature and saturation as variables usually use rocks and rarely involve coal. However, some differences between rock and coal exist; rock is strong and hard with weak water absorption, while coal is a softer material with greater porosity. The mineral composition of coal is also very different from that of rock. Frozen coal and frozen rock in the static-load state have been extensively studied. However, research on dynamic-load impact is limited, and research on the destruction process is even more limited. In underground frozen mining, the difference in mining temperature and water saturation rate often leads to certain deformations.