## 3 Analysis of Test Results
### Fractal Characteristics of Crushing Products  
To better analyse the result after sample destruction, and referring to the relevant standards [32], the sample sieves with 9.50 mm, 4.75 mm, 2.36 mm, 1.18 mm, 0.60 mm, 0.30 mm, 0.15 mm, 0.075 mm, and eight grades were combined in the order of largest to smallest. The coal and rock after SHPB impact damage were sieved on site. A high-precision balance was used to weigh the broken pieces of coal and rock for each rank. The statistical results are summarised in Tables 3 and 4. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample No. **} & **Impat Speed** & \multicolumn{6}{c}{**Cumulative Mass Percent of Each Particle Size Under the Sieve\%\%**} & \multicolumn{6}{c}{**Fitting Results**} & \multicolumn{1}{c}{**Fractal Dimension**} \\ \cline{2-13}  & **(m/s)** & **0.075** & **0.15** & **0.3** & **0.6** & **1.18** & **2.36** & **4.75** & **9.5** & **F  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample No. **} & \multicolumn{4}{c}{**Impact Speed**} & \multicolumn{4}{c}{**Cumulative Mass Percent of Each Particle Size Under the Siew/\%**} & \multicolumn{4}{c}{**Fitting Results**} & \multirow{2}{*}{**Fractal Dimension**} \\ \cline{2-2} \cline{4-13}  & **(m/s)** & & & & & & &  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample No. **} & \multirow{2}{*}{**Impact Speed**} & \multicolumn{6}{c}{**Cumulative Mass Percent of Each Particle Size Under the Sieve/\%**} & \multicolumn{6}{c}{**Fitting Results**} & \multirow{2}{*}{**Fracial Dimension**} \\  & **(m/s)** & & **0.075** & **0.15** & **0.3** & **0.6** & **1.18** & **2.36** & **4.75** &  
Notably, some of these values were discarded because most of the rock samples did not undergo significant damage at an impact of 10 m/s and were not of screening significance. Referring to Equation (7), a double logarithmic expression for the impacted samples was established and regression analyses were performed. The results are shown in Figure 14. Combining Tables 3 and 4 shows that there is a good logarithmic correlation between the cumulative mass percentage of the sub-screen particle size and the sample sieve diameter. The correlation coefficient was very high, which indicated that the post-crushing lump size distribution of this coal and rock samples were self-similar to a fractal distribution. The fractal dimension fluctuates between 1.29 and 2  
Figure 14a shows the mass fractal dimension of coal at the same temperature (\(-20\)\({}^{\circ}\)C) and different saturation and velocity conditions. From the figure, the following can be observed: (1) Under the same saturation conditions, with increasing impact velocity, the slope of the fitted curve of the raw coal sample gradually decreases and the value of the mass dimension gradually increases. This result indicates that with increasing velocity, the degree of sample devastation increases and the degree of fragmentation rises. (2) At an impact velocity of 6 m/s, the fitted slope of the dry state is lower than that of the saturated state, which indicates that the mass dimension number in the saturated state is lower than that in the dry state. The crushing volume is larger in the saturated state. Figure 14b shows the mass fractal dimension of the rocks at the same temperature (\(-10\)\({}^{\circ}\)C) under different saturation and velocity conditions. Figure 14b exhibits a similar pattern to Figure 14a, where both velocity and saturation have a similar effect on the coal and rock samples. However, the slopes of the raw rock samples are higher than those of the raw coal samples, indicating that at the inflection point of \(-10\)\({}^{\circ}\)C, the rock is still more brittle than the raw coal.