## 5 Conclusions  
In this study, coal and rock are taken as research objects; water, temperature, and dynamic load are taken as variables; and multifractal technology is used to analyse the failure trends of coal and rock. The following conclusions are drawn:  
(1) The dynamic mechanical properties of coal and rock samples under the SHPB impact process are affected by their own physical properties, temperature, saturation degree, and impact velocity under joint action. When measuring the longitudinal wave velocity, the rock samples (2.24-2.61 km/s) have lower wave velocities than the coal samples (1.68-2.01 km/s). With decreasing temperature, both the coal and rock samples show a trend of initially increasing and then decreasing, with an \"N\"-shaped pattern. Comparing the samples in the dry state and saturated state, the wave velocities of the coal and rock samples in the saturated state are higher than those of the coal and rock samples in the dry state. (2) The peak stress-temperature curve and stress-strain curve are plotted after noise reduction of the stress curve. The higher density of the specimen at the same impact velocity correlates to a faster propagation of the stress wave. With the increase in impact velocity, the strain intensification gradually becomes evident. Under the influence of speed and temperature, the influence factor of speed is greater. (3) In the dynamic impact damage process of the coal and rock, the box dimension has evident self-similarity. The quantitative description of the cracks in the box dimension of the coal and rock specimens shows an overall increase and local oscillation; additionally, the dimension number of the dry samples is higher than that of the saturated condition under the same impact velocity with a fast end time. In the same saturated condition, the value of the box dimension increases with increasing impact velocity without shortening the duration. Comparing coal and rock, the holding time of the whole rock is shorter than that of the coal sample, and the final value of the box dimension number is smaller than that of the original coal. (4) After sieving the impacted coal and rock samples and calculating the mass dimension number, a linear positive logarithmic correlation is observed between the cumulative mass percentage of the sub-screen grain size and the sample sieve diameter. The correlation coefficient is large and indicates that the post-crushing mass distribution of the coal and rock samples is self-similar to a fractal distribution. The fractal dimension fluctuates between 1.29 and 2.26. The slope of the fitted curve decreases with increasing impact velocity and decreasing saturation. Raw coal and raw rock are also affected to different degrees by different temperatures. (5) Through microscopic analyses, it can be concluded that when the inside of the coal or rock is filled with a large number of water molecules, the decrease in temperature will cause the internal coal or rock matrix to contract, thus increasing its densification, and when the water freezes into ice, due to its ice uplift force, it results in expansion and deformation of the inside of the coal or rock. The two influence each other and the dominant factors are different at different temperatures. It should be noted that this paper has initially explored the damage characteristics of coal and rock bodies with temperature, water, and dynamic loading and its influencingfactors using SHPB; however, further exploration, such as triaxial impact experiments under variable temperatures, freeze-thaw cyclic impact experiments, the main influencing factors subjected to the freezing method when drilling wells and tunnelling, etc., still need to be studied more deeply. Conceptualisation, X.S. ; Methodology, K.L. ; Software, S.L. ; Validation, S.Y. ; Writing\(-\)review and editing, J.X. ; Writing\(-\)original draft, T.J. All authors have read and agreed to the published version of the manuscript.