## 3 Results and Discussion
#### 3.2.1 Stress Analysis of Gangue Particles
The relevant data are calculated by screening processing. Figure 12 shows the effect of the fractal dimension on the solid mass fraction \(W\) of the slurry. The analysis shows that the larger the fractal dimension is, the smaller the range of change of the solid mass fraction in the process of slurry settlement is, and the gentler the settlement behavior is. In the upper area of the settlement instrument, with the extension of the settlement time, the solid mass fraction of all slurry showed a downward trend, and the larger the fractal dimension, the smaller the decrease in the solid mass fraction. This is because as the fractal dimension increases, the proportion of fine particles gradually increases, the gap between particles in the slurry decreases, and the filling effect between particles increases. The filling effect increases the friction between particles and hinders the free settlement of particles. The filling effect of fine particles will increase the overall density of the slurry, resulting in a slower sedimentation rate. In the central area of the sedimentation instrument, the solid mass fraction of the slurry with fractal dimension \(D=2.7\) increased after settling for 5 min. In contrast, slurry with fractal dimensions \(D=2.3\)-\(2.6\) showed a continuous decrease in the solid mass fraction, and the change in the solid mass fraction in this area was relatively gentle. This is because the settled particles in the upper area have settled in the lower area. When the content of fine particles in the slurry is high, the interaction between the particles and the liquid will gradually slow down the settling velocity and eventually stabilize. In the lower area of the sedimentation instrument, the solid mass fraction of each slurry increases with time, and the larger the fractal dimension, the smaller the increase in the solid mass fraction. This is because the lower part of the settler will first accumulate large particles. With time, smaller particles will gradually reach the lower part, increasing the mass fraction of the lower part. [PERSON] et al. [59] pointed out in their study that in order to improve the time-dependent suspension stability of slurry during pipeline transportation, methods such as increasing the amount of fine-grained particles are usually used. Correspondingly, this study found that when the fractal dimension of the slurry is larger, the proportion of fine particles in the slurry is also more significant, which is consistent with the conclusion in the research results, i.e., in the slurry with a larger fractal dimension, the increase in the solid mass fraction in the upper region is smaller. This indicates that the increase in the proportion of fine particles helps to improve the stability of the slurry and may inhibit the drastic change in the solid mass fraction to a certain extent. Figure 11: Particle distribution diagram during the process of slurry settlement. Figure 13 shows the dynamic fractal distribution \(D_{\rm S}\) of particles in different regions of the slurry with different fractal dimensions during the settlement process. The analysis shows that the smaller the fractal dimension of the original slurry, the more significant the particle size distribution changes. In the upper area of the sedimentometer, for the slurry with \(D=2.3\)-\(2.7\), the \(D_{\rm S}\) shows an upward trend with the settlement process, and with the increase in the original fractal dimension, the change range of the fractal distribution gradually decreases. This is because the gangue with a large particle size settles fastest in the process of slurry settlement, resulting in a rapid decrease in the content of large particles in the upper region [60]. In the middle area of the sedimentation instrument, the particle distribution \(D\)s of the slurry with a fractal dimension of \(2.3\) showed a significant downward trend with the sedimentation time. Still, the decline was gentler than in the upper area.