## 3 Results and Discussion
### Superiority Verification of the Optimized DDARF Program
#### 3.2.2 Analysis of Model Cracking Process  
In the experimental process, the models of the three cases showed similar rules: after loading, the models first demonstrated compression deformation, and the preset joints display compaction. With the progress of compression, the ends of the preset joints cracked, and wing cracks appeared (Figures 10a, 11a and 12a). The wing cracks expanded in the direction of the large principal stress (Figures 10b, 11b and 12b). The width of the wing crack increased with the load increase (Figures 10c, 11c and 12c). The propagation of the upper wing cracks extended in the axial direction through the top of the model; a group of new oblique parallel cracks appeared on the preset joints (Figures 10d, 11d, and 12d). At the same time, some fine cracks appeared in the model, which expanded with the increase in pressure, and the fine cracks became connected with the wing cracks and preset joints (Figures 10e, 11e and 12e), which finally led to the failure of the model. The above analysis shows that the optimized DDARF program can effectively simulate the uniaxial compression experiment of rock blocks.  
Figure 9: Rock models after grid generation for three cases: (**a**) Case 1; (**b**) Case 2; (**c**) Case 3.  
However, there are some subtle differences among the three models in the expansion of the joint, as follows: in the process of the expansion of the preset joint, after the wing cracks appeared at the ends of the preset joints of the Case 1 model, wing cracks expanded along the axis and secondary joints did not appear near the ends of the preset joint, as shown in Figure 10b-e. In the model of Case 2, after the wing cracks appeared at the end of the preset joint, some secondary joints appeared near the left end of the preset joint during the expansion of the wing cracks. The increase and expansion of secondary joints resulted in the fragmentation of the rock mass at the left end of the preset joint, as shown in Figure 11c-e. This failure rule is consistent with the numerical simulation results of other scholars, as shown in Figure 13 [30]. The reason for these kinds of failure rules is that the grids generated near the preset joints in Case 2 are relatively dense and can show more subtle changes. In the model of Case 3, secondary joints also appear at the left end of preset joints in the process of wing crack propagation, resulting in the fragmentation of rock mass in this part, as shown in Figure 12c-e, indicating that the accuracy of simulating rock block failure in Case 2 is close to that in Case 3.  
Figure 11: Failure process of Case 2 in uniaxial compression simulation experiment. (**a**) The ends of the preset joints cracked and wing cracks appeared; (**b**) Wing cracks expanded; (**c**) The width of the wing crack increased and fine cracks and some secondary joints appeared; (**d**) A group of new oblique parallel cracks appeared; (**e**) The fine cracks became connected with the wing cracks and preset joints.  
Figure 10: Failure process of Case 1 in uniaxial compression simulation experiment. (**a**) The ends of the preset joints cracked and wing cracks appeared; (**b**) Wing cracks expanded; (**c**) The width of the wing crack increased and fine cracks appeared; (**d**) A group of new oblique parallel cracks appeared; (**e**) The fine cracks became connected with the wing cracks and preset joints.  
In short, the failure process of rocks can be more carefully simulated in Case 2 than in Case 1, and the results are closer to those of other scholars. The joint expansion law of Case 2 in the dense grid region is close to that of the Case 3 model with a large number of uniform grids. The above analysis shows that the optimized DDARF has advantages in simulating the law of joint expansion.