# Study on the Macro-Fine Mechanical Behavior of Ore Flow Based on the Discrete Element Method
## 4 Flow Characteristics and Stress Distribution of Ore-Rock Bulk
### Stress Distribution of the Ore-Rock Bulk  
#### 4.2.1 Contact Density of Ore-Rock Bulk  
The coordination number (\(Z_{i}\)) is the average contact number between the particles of the ore-rock bulk, which reflects the quality and density of the internal contact of ore-rock particles to a certain extent. Therefore, the evolution law of internal micromechanics in ore-rock particles' flow process can be directly studied by analyzing the coordination number [35]. The formula for calculating coordination number is as follows [36]:  
\[Z_{i}=\frac{2N_{C}}{N_{P}} \tag{1}\]  
where \(N_{C}\) is the actual contact number of bulk particles (normal contact force is greater than 0) and \(N_{P}\) is the total number of particles in the bulk. It should be noted that when the number of contacts of a single particle is only 1, or there is no other particle in contact with it, it is considered that this particle has no contribution to the micromechanics of the entire particle system and should be ignored. In order to facilitate the statistics of the coordination number changes in each labeling layer, the average value of the coordination number \(Z_{a}\) is introduced, and its calculation formula is as follows:  
\[Z_{a}=\frac{\sum\limits_{i=1}^{3}Z_{i}}{3} \tag{2}\]  
According to the coordination \(Z_{a}\) obtained by the monitoring during the numerical simulation, the change curve of the average value of the labeling-particle layer at different ore-drawing times was drawn, as shown in Figure 7. The coordination numbers monitored by 1-6 measurement circles were divided into Group 1, those measured by 7-12 were divided into Group 2, and those measured by 13-18 were divided into Group 3. It can be seen from Figure 7 that the average coordination numbers at different positions in the ore-rock bulk are different to some extent during the whole ore-drawing process--the closer to the bottom of the ore pass, the greater the average coordination number, which also indicates that the ore-rock bulk is more compact. This phenomenon reflects the influence of the action of ore-rock particles' gravity. It can also be seen from Figure 7, that before the ore drawing begins, the average coordination number of Groups 1 to 3 is about 3.84-4.15, 3.72-3.2-4.05, and 3.21-3.68, respectively. The change relationship of the coordination numbers of different groups is Group 3 \(>\) Group 2 \(>\) Group 1, while the corresponding coordination number of each group has the opposite fluctuation rule. When the ore-rock was drawn five times, the coordination numbers of Group 1 gradually increased from 3.41 to 3.87, that of Group 2 fluctuated to decrease and was similar to the change rule of the coordination numbers without ore drawing, and that of Group 3 decreased rapidly from 3.54 to 0. When ore drawing 10 times, the coordination numbers of Group 1 increased from 3.44 to 3.85, and those of Group 2 and Group 3 decreased exponentially with the increase in the number of measurement circles and finally stabilized at about 0. With the increase in the ore-drawing times, the change rule of the coordination numbers of each group is almost consistent, decreasing exponentially to 0. According to the above analysis, it can be seen that due to the effect of the inertia force generated by the particles flowing and the bulk gravity of ore-rock bulk in the range of Groups 2 and 3 during the entire ore-drawing process, the ore-rock particles' coordination numbers in the range of the measurement circles of Group 1 fluctuate and then decrease. This indicates that the ore-rock particles in this region tend to have a state of compact contact with high contact strength compared to that of loose contact with small contact strength. Affected by the ore-rock drawing out, the coordination number of Group 2 is lower than that of Group 1, the ore-rock particles move toward having a dense contact strength with high strength from having loose contact with low strength, but the degree is not as high as that of Group 1.