## 4 Analysis of Grain Shape Effects
### Effects of Grain Shape on Rock Macroscopic Parameters  
Figure 7 shows the effects of grain shape on rock peak strength and elastic modulus. It can be seen that the peak strength and elastic modulus of the model with the strip-shaped grain was the largest, followed by the triangular grain and square grain models. Compared with the circular grain (shape number 1), the elastic modulus of the models with clumped grains was significantly increased (shape numbers 2-6). According to our simulated results, the effects of grain shape on rock peak strength and elastic modulus were closely related to the model's porosity. Figure 8 shows the effects of grain shape on porosity. It can be seen that the porosity of the square grain model was the largest, followed by the triangular grain and strip-shaped grain models, contrary to the variation of peak strength and elastic modulus. It can also be seen from Figure 7a that with the increase of the _d/R_ value, the peak strength of the models with strip-shaped and triangular grains first increased and then decreased, but it only decreased when the grain shape was square. This variation was closely related to the flatness and roughness of the mineral grain. Firstly, as can be seen in Figure 5a, the flatness of the strip-shaped grain was obviously higher than that of the triangular and square grains. Also, the peak strength of model with strip-shaped grains was significantly higher, indicating that an increase in flatness can enhance rock peak strength, which was mainly because the strip-shaped grains were difficult to rotate and displace when they were assembled together. [PERSON] et al. [39] also thought that a model with strip-shaped grains would have higher strength. Secondly, because the flatness of the square and triangular grains was significantly lower (Figure 5a), the overall contour was close to circular. Therefore, the peak strength was slightly affected by flatness in the models with square and triangular grains. However, the grain surface roughness was relatively higher, and the main influencing factor affecting the peak strength was roughness. As can be seen from Figure 7a, the peak strength decreased with increasing roughness. Therefore, the variations of rock peak strength shown in Figure 7a were due to the combined effects of mineral flatness and roughness. The effects of shape factors on the peak strength of models with different grain shapes are discussed in detail as follows:  
1. Strip-shaped grain  
It can be seen from Figure 5 that when the _d/R_ value was low, the surface roughness of the strip-shaped grain increased slowly, but the flatness increased rapidly. Therefore, the obvious increase of peak strength from models S1 to S3 was mainly controlled by the flatness. When the _d/R_ value became higher, the roughness increased rapidly, and the peak strength decreased significantly, indicating that the peak strength was mainly affected by the roughness from models S4 to S6. It can be concluded that when the roughness exceeds a certain limit, it will be the main factor of strength change. Figure 8: Effects of grain shape on rock porosity. Figure 7: Effects of grain shape on rock (**a**) peak strength and (**b**) elastic modulus. 2. Triangular grain  
When the _d_/_R_ value was low (shape numbers T1-T3), similar to the model with the strip-shaped grain, the increase of peak strength of models with triangular grains was also controlled by the flatness. However, because the increase of the flatness of triangular grain was much lower than that of the strip-shaped grain, the increase of peak strength of models with triangular grains was also obviously lower than that of the models with strip-shaped grains. When the _d_/_R_ value was higher (shape numbers T4-T6), the decrease of the peak strength was affected by the increasing roughness. 3. Square grain  
For the models with square grains, the decrease of the peak strength was controlled by the roughness. The roughness increased slowly from models R1 to R3, which led to the slow decrease of the peak strength.