## 3 Results
### Micro Behavior Analysis  
#### 3.2.1 Contact Network Characteristics  
* Coordination number  
The coordination number is the average number of collisions between each particle and the surrounding particle, which can well reflect the density and internal stability of the particle aggregate. [PERSON] [19] concluded that the particles with less than two collisions have basically no contribution to the stable stress state, so the mechanical average coordination number is used. The calculation formula is:  
\[Z=\frac{(2C-N_{1})}{(N-N_{0}-N_{1})} \tag{5}\]  
where \(C\) is the total number of collisions inside the particle aggregate; \(N\) is the total number of particles inside the specimen; \(N_{0}\) is the number of particles with 0 collisions; \(N_{1}\) is the number of particles with 1 collision. Figure 10 shows the coordination number-axial strain curve of thirteen different gravel-shaped particles at 200 kPa. As illustrated in Figure 10, the average coordination number exhibits a significant declining trend throughout the loading process. It decreases rapidly with increasing axial strain and eventually stabilizes at a constant value. With decreasing EI and FI, the coordination number of granule aggregate increased and enhanced the degree of granule interlocking, with a more stable contact force strand and a higher shear strength of granule aggregate, which is consistent with the results in Figure 4.  
Figure 8: Maximum dilatancy angle of specimens with different particle shapes: (**a**) EI; (**b**) FI; and (c) EI/FI. Figure 9: Particle arrangement changes during the shearing process: (**a**) EI = FI = 1; (**b**) EI = FI = 0.6. * Probability density The contact force between the particles was calculated as follows: \[f=f_{n}\mathbf{n}+f_{t}\mathbf{t}\] (6) where \(f_{n}\), \(f_{t}\) are the normal and tangential components of the contact forces, [N]; \(\mathbf{n}\) and \(\mathbf{t}\) are the unit vectors of \(f_{n}\) and \(f_{t}\). The distribution characteristics of the contact network inside the particle assembly can be characterized by the probability density of the contact force \(f_{x}\) between particles. [PERSON] et al. [34] found that the probability density function of the normalized normal contact force \(\frac{f_{n}}{\langle f_{x}\rangle}\) presents an exponential function change in the strong contact part and a power-law change in the weak contact part. The calculation formula is:  
\[P(f_{x})\propto \begin{cases}e^{-A(\frac{f_{x}}{\langle f_{x}\rangle})},f_{x} >\langle f_{x}\rangle\\ \left(\frac{f_{x}}{\langle f_{x}\rangle}\right)^{B},f_{x}<\langle f_{x}\rangle \end{cases}  \tag{7}\]  
where \(f_{x}\) is \(f_{n}\) or \(f_{t}\), [N]; \(\langle f_{x}\rangle\) is the average of \(f_{n}\) or \(f_{t}\), [N]; A and B are the correlation coefficients. 1. Normal and tangential contact forces Figures 11 and 12 show the relationship curves of the normalized normal contact force \(\frac{f_{n}}{\langle f_{n}\rangle}\) probability density function at 200 kPa. The internal illustration shows the correlation coefficients A and B with EI and FI, the correlation coefficient A shows a downward trend with the increase in EI and FI, and the correlation coefficient B shows an upward trend with the increase in EI and FI. Combining Figures 11 and 12 shows that the probability density decreases as the normalized normal contact force \(\frac{f_{n}}{\langle f_{n}\rangle}\) increases. The normalized probability density distribution associated with different EI is more discrete at \(\frac{f_{n}}{\langle f_{n}\rangle}>3\), indicating that the normal contact force is less uniformly distributed at large strong contact forces. When \(1<\frac{f_{n}}{\langle f_{n}\rangle}<3\), the difference in probability density is not obvious, indicating a normal contact force where the strong contact force is less affected by EI and FI.