## 3 Results and Discussion
### Particle Velocity Distribution  
The simulation showed the effects of rake angle and belt motion on particle velocity distribution (9). The magnitude distribution of particle velocity changed as the rake angle increased (Figures 9a-d and 9e-h, respectively). The particles with the highest velocities (close to 1 m/s, red) gradually occupied the entire tool face, and gradually replaced the particles with medium velocities (0.33 to 0.78 m/s, yellow to green). While the particles with the lowest velocities (close to 0 m/s, blue) barely changed. However, there were differences in the magnitude distribution of particle velocity between the belt tools and the regular tools at the same rake angles. The belt tools had more low-velocity particles (yellow to green) in their vicinity than the regular tools when the rake angles were 30\({}^{\circ}\) and 45\({}^{\circ}\) (Figures 9a,b and 9e,f, respectively), but more high-velocity particles instead (close to 1 m/s, red) in the cases of the rake angles 60\({}^{\circ}\) and 75\({}^{\circ}\) (Figures 9c,d and 9g,h, respectively).  
The particle velocity showed a correlation between its magnitude and direction distributions (Figure 13). The particle velocity vectors mostly pointed obliquely at the soil surface  
Figure 11: Angle of Rupture (\(\beta\)).  
Figure 12: Rupture distance (\(L\)).  
in front of the tool. The average vector direction in the grid cells ranged from 0 to 50\({}^{\circ}\) (yellow to green cells). There were more particles moving in lower directions as the rake angle increased (Figures 13a-d and 13e-h, respectively). The particles moving in average directions lower than 30\({}^{\circ}\) (green) gradually replaced those higher than 30\({}^{\circ}\) (yellow) and gradually occupied the entire tool face. However, the belt tools had more particles moving in average directions higher than 30\({}^{\circ}\) (yellow) than the regular tools (Figures 13a,e, 13b,f, 13c,g and 13d,h, respectively). The results show that the belt motion leads to an increase in the direction of particle velocity.  
The above results indicate that the distribution of particle velocity in the longitudinal section is affected by the rake angle and the belt motion. A larger rake angle results in more forward particle movement, while the belt motion makes more particles move upwards. A typical soil particle velocity in the vicinity of the tool face usually has a large horizontal component that is close to the operating speed of the tool. This makes the particles move slowly relative to the tool face. Then, a soil buildup develops on the tool face [19]. The buildup is considered to be negative to subsoiling. It reduces the rate of soil replacement in the disturbance zone, and changes the tool shape. Also, it may intensify the soil compression in the disturbance zone and increase the friction on the tool surface [24]. These all result in an increase in draught force. However, the belt motion leads to more soil particles in deep layers escaping to the free surface as well as the soil in the disturbance zone being rapidly replaced by subsequent soil, which reduces the soil compression in the disturbance zone. This is another reason for the reduction in draught force.