## 3 Results and Discussion
#### 3.1.1 Analysis of Mini-Slump, Expansion, and Bleeding Rate  
The influence of the fractal dimension on the mini-slump and expansion of CSFMs is presented in Figure 5. The mini-slump and expansion of CSFMs have similar trends, both of which increase first with the increase in the aggregate fractal dimension. When the fractal dimension exceeds 2.50, the mini-slump and expansion of CSFMs begin to decrease. This is because when the particle fractal dimension \(D\) increases, the proportion of large-particle gangue in the slurry decreases. This reduces the sliding friction of large particles in the mud flow process, thereby improving the fluidity. As the fractal dimension \(D\) of particle gradation continues to increase, the fraction of small gangue particles in the slurry increases, the system gradation deteriorates, and the slurry viscosity rises. Therefore, liquidity deteriorates [41]. Increased friction and particle collisions caused by tiny particles are another critical factor contributing to decreased fluidity [42; 43]. In the reference paste filling, the minimum slump value is 100 mm. When the value is better than 160 mm, it is considered to have good fluidity. The slump values equivalent to a mini-slump cylinder are 44.4 mm and 70.8 mm, respectively [44]. Therefore, when using slump and expansion to evaluate the fluidity of coal gangue slurry, CSFMs with \(D\) = 2.3-2.7 exhibit good fluidity, meeting the requirements for pipeline transportation.  
Figure 5 illustrates the influence of the fractal dimension on the bleeding rate of CSFMs. The analysis shows that the bleeding characteristics of CSFMs can be effectively adjusted by controlling the fractal dimension, and the bleeding rate has a significant negative correlation with the fractal dimension. This is due to the fact that a smaller fractal dimension, \(D\), corresponds to a higher proportion of large particles in the gradation. When the proportion of large particles increases, the pore structure inside the slurry will increase. Free water will fill these voids and escape from the voids after standing for a period of time [45]. The bleeding rates of CSFMs with \(D\) = 2.3 to 2.7 were 7.61%, 6.63%, 4.88%, 3.24%, 3.15%, 3.02%, and 1.88%, respectively. Combined with the filling engineering practice of Shenzhou Coal Industry, when the bleeding rate of filling slurry exceeded 5%, slurry segregation and plugging accidents occurred, meaning that requirements for the safe  
Figure 5: Effect of the fractal dimension on the slump, expansion, and bleeding rate of slurry.  
transportation of slurry cannot be met [46]. Therefore, when the bleeding rate is used to evaluate the flow performance of coal gangue, the five groups of \(D=2.45\), \(D=2.50\), \(D=2.55\), \(D=2.60\), and \(D=2.70\) can meet the requirements of pipeline transportation. On the other hand, \(D=2.3\) and \(D=2.4\) cannot meet the requirements of pipeline transportation.  
Based on the above research, when slump and expansion are used to evaluate the fluidity of coal gangue slurry, \(D=2.3\) and \(D=2.4\) can meet the requirements for gangue filling pipeline transportation fluidity. Conversely, when the bleeding rate is used to evaluate the fluidity of coal gangue, \(D=2.3\) and \(D=2.4\) cannot meet the requirements of pipeline transportation. It can be seen that it is difficult to accurately evaluate the fluidity of gangue slurry by using a single slump or bleeding rate index. Fractal dimension is a parameter related to the slump and bleeding rate, which has technical advantages in evaluating the fluidity of gangue slurry.