## 3 Implementation and Application of DFN Simulation of the Rock Mass
### Example of Application  
We applied the proposed method to the high rock-slope engineering of the Baiyunebo eastern iron open pit in Inner Mongolia to illustrate its feasibility, and analyzed the results of the simulation.  
According to the relevant literature [30], the fractures of this slope can be divided into four groups, and the characteristic statistical values of the parameters of the geological model of each group are shown in Table 1. The scales of the study domain in the \(x\), \(y\), and \(z\) axes were all taken to be 20 m.  
Figure 4 shows the results of the 3D DFN model based on the proposed method using the data in Table 1. Figure 4a reflects the spatial cross-cutting relationship of each group of rectangular fractures, and Figure 4b reflects the spatial cross-cutting relationship between fractures and the boundary of the study domain.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Group**} & \multirow{2}{*}{**Dip Direction/(\({}^{\circ}\))**} & \multirow{2}{*}{**Dip Angle/(\({}^{\circ}\))**} & \multicolumn{2}{c}{**Trace**} & \multirow{2}{*}{**Linear**} \\  & & & & & **Length/(m)** & \\ \cline{2-2} \cline{5-6}
**Fractures** & \multirow{2}{*}{**Mean**} & \
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} & \multirow{2}{*}{**Mean**} &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} & \multirow{2}{*}{**Mean**} & \multirow{2}{*}{**Density/(1/m\({}^{3}\))**} \\ \hline A & 232.50 & 23.38 & 58.00 & 16.17 & 11.90 & 0.32 \\ B & 323.41 & 17.24 & 68.92 & 14.10 & 12.20 & 0.35 \\ C & 76.40 & 26.01 & 75.57 & 8.14 & 9.78 & 0.45 \\ D & 171.43 & 12.30 & 70.77 & 6.94 & 10.03 & 0.87 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Characteristic statistical values of the geological parameters of fractures.  
Figure 3: Flow of implementation of the DFN simulation, and the relationship between modules.  
Figure 5 shows the results of the DFN model in comparison with the measured fractures. Figure 5a reflects the distribution of the measured fractures on an outcropping surface of the high rock slope of the Baiyunebo eastern iron open pit in Inner Mongolia, and Figure 5b shows the distribution of fractures obtained by the DFN model on the boundary of the study domain. In general, the DFN simulation ought to identify statistical laws and construct a sample-based fracture network according to random information, where this is not equivalent to a real fracture network and is only statistically similar to it in the mathematical sense. From this perspective, the 3D DFN model based on the Monte-Carlo technique exhibited good statistical similarity i to the actual distribution of fractures at the engineering site on a 2D representative surface in terms of the orientation, scale, and density of fractures. This proves that the proposed method of simulation of the 3D DFN is reasonable and effective.  
Figure 4: 3D DFN model. **(a)** Spatial cross-cutting relationship of each group of fractures; **(b)** spatial cross-cutting relationship between fractures and the boundary of the study domain.  
Figure 5: Comparison of images of fractures between the DFN simulation and the measurements on site. **(a)** Measured distribution of fractures on the outcropping surface; **(b)** distribution of fractures obtained by the DFN model on the boundary of the study domain.