## 3 Results and Discussion
### Accuracy Verification of the Optimized DDARF Program
#### 3.1.2 Analysis and Comparison of Results  
After loading, vertical main cracks appeared firstly in the top and bottom of the model, as shown in Figure 5b;with the load continuing, some secondary cracks appeared next to the main cracks which were at the top and the bottom of the model, as shown in Figure 5c, which is consistent with [PERSON]'s research (pp. 60-61, [28]). As the load continued to increase, the vertical main cracks which first appeared continued to expand vertically (Figure 5d), and finally the vertical main cracks broke through, resulting in the destruction of the model (Figure 5e).  
Figure 6 is the physical experiment of the Brazilian disc-splitting experiment (pp. 80-82, [8]). It can be seen that, after the experiment, a crack appears in the middle of the disc, which divides the disc into two parts; the failure characteristics of the physical experiment are consistent with those of the Brazilian disc-splitting experiment simulated by the optimized DDARF, which verifies the effectiveness of the optimized DDARF in rock simulations. To compare with the results of the Brazilian disc-splitting experiments simulated in the original DDARF by [PERSON] (p. 61, [28]) as shown in Figure 7, it can be seen that the destruction of the model law is consistent, and because the optimized DDARF program defined the grid density of crack initiation and expansion area, it can simulate more subtle crack initiation in the splitting process of the Brazilian disc, as shown in Figure 5e.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Density** \\ **(kg/m3)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Elastic** \\ **Modulus** \\ **(GPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Elastic** \\ **Modulus** \\ **Uniformity** \\ **Coefficient** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Poisson's** \\ **Ratio** \\ **Ratio** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Poisson's** \\ **Uniformity** \\ **Coefficient** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Poisson's** \\ **Uniformity** \\ **Coefficient** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Friction** \\ **Angle (\({}^{\circ}\))** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Cohesion** \\ **Strength** \\ **(MPa)** \\ \end{tabular} } \\ \hline
2500 & 70 & 15 & 0.3 & 100 & 30 & 40 & 15 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mechanical parameters of the Brazilian disc model.  
Figure 4: Geometric parameters and loading mode of the model.  
Figure 5: Optimized DDARF simulates the disc failure process of the Brazilian disc-splitting experiment: (**a**) The model in optimized DDARF; (**b**) Vertical main cracks appeared firstly in the top and bottom of the model; (**c**) Some secondary cracks appeared next to the main cracks; (**d**) Vertical main cracks continued to expand vertically; (**e**) Vertical main cracks broke through, resulting in the destruction of the model.  
Figure 6: Failure results of specimens in Brazilian splitting physical experiment.