## 3 Results
### Micro Behavior Analysis
#### 3.2.1 Contact Network Characteristics
When \(\frac{f_{n}}{\langle f_{n}\rangle}<1\), the particle aggregate's weak contact probability density slightly decreased with the increase in EI and FI, the particles for the ideal sphere (\(EI=FI=1\)), and the weak contact force probability density is significantly reduced, suggesting that the more particles in the ideal-sphere particle aggregate that are used to support the external load, the weaker the reduction in the weak contact force ratio of ideal-sphere specimen force-chain stability, which is also reflected in the fact that the ideal sphere finds it more difficult to carry out particle interlocking, indicating that the overall stability of the specimen is weak. Figure 10: Coordination number–axial strain curves of specimens with different particle shapes (200 kPa): (**a**) EI; (**b**) FI and (**c**) EIFI. Figures 13 and 14 show the relationship curves of the normalized tangential contact force \(\frac{f_{t}}{\langle f_{t}\rangle}\) probability density function at different scales and different EI/FI at 200 kPa. The internal insects show the correlation coefficients A and B with the relationship curve between EI and FI, and the overall law is similar to the normal contact force. 2. Mobilized contacts  
For granular materials, the shear strength of the particle assembly is affected by the degree of friction sliding of the internal particles, which can be characterized by the friction mobilization index [35]. The calculation formula is as follows:  
\[I_{m}=\frac{|f_{t}|}{\mu f_{n}} \tag{8}\]  
where \(\mu\) is the friction coefficient; \(|f_{t}|\) is the tangential contact force, [N]; \(f_{n}\) is the normal contact force, [N]. Figure 11: Probability density function of normal contact force for specimens with different particle shapes (200 kPa, 60% axial strain, in log–linear scale): (**a**) EI; (**b**) FI; and (**c**) EI/FI. Figure 12: Probability density function of normal contact force for specimens with different particle shapes (200 kPa, 60% axial strain, in log–log scale): (**a**) EI; (**b**) FI; and (**c**) EI/FI. Figure 13: Probability density function of tangential contact force for specimens with different particle shapes (200 kPa, 60% axial strain, in log–linear scale): (**a**) EI; (**b**) FI; and (**c**) EI/FI. Figure 15 shows the friction-play exponential probability distribution function between different EI and FI at the pressure of 200 kPa. As shown in Figure 15, the probability density of the particles is high at \(I_{m}<0.7\), and the distribution of \(I_{m}\) is relatively more uniform, where \(\langle I_{m}\rangle\) is the average of the specimen friction play index. It can be seen that with the decrease in EI and FI, the \(\langle I_{m}\rangle\) of the particle aggregate gradually increases, which reflects that the more the particle shape of the constituent specimen deviates from the sphere, the higher the friction mobilization in the particle aggregate, and the more likely the particle interlocking, which is consistent with the macroscopic law mentioned above. When I\({}_{\text{m}}>0.9999\), the contact between particles is defined as sliding contact. Figure 16 shows the sliding contact-axial strain curve of the specimens with different EI and FI at a lateral pressure of 200 kPa. The figure shows that sliding contacts increase rapidly with rising axial strain, peak at approximately 1% axial strain, and then gradually stabilize as shearing progresses. Furthermore, the proportion of sliding contacts increases as EI and FI decrease. The results of EI part of this study were consistent with those of [PERSON] et al. [31] and [PERSON] et al. [26]. * Strong contacts If the normal contact force \(f_{n}\) is greater than the average contact force \(\langle f_{n}\rangle\), it is defined as a strong contact. Figure 17 shows the strong contact-strain curves under different EI and FI at a lateral pressure of 200 kPa.