# Deterministic Discrete Fracture Network Model and Its Application in Rock Mass Engineering
## 3 Example Verification  
Dan Shan Station is located at the intersection of Heilongjiang Middle Road and Shimei'an Road. The strata mainly consist of a slightly weathered granite layer and moderately weathered tuff layer, with burial depths of approximately 23.2 m and 19.15 m, respectively. The rock mass grades are IV and V. The sampling area is primarily within the slightly weathered granite layer and the moderately weathered tuff layer. The following explanation will use pile number K16+790.5 as an example. First, based on the collected point cloud, a raster model of the rock mass area is constructed, as shown in Figure 5.  
After obtaining the raster model, extract its slope, aspect, and elevation standard deviation. Perform ISODATA clustering on the slope, aspect, and elevation standard deviation, as shown in Figure 6. After clustering and zoning, filter the noisy clustering results using a window size greater than 20, as shown in Figure 7.  
After removing smaller clusters through filtering, the DEV results for the remaining clustered zones were calculated, as presented in Table 3. The degree of surface undulation of the structural plane calculated by \(DEV\) can be normalized to represent the local surface roughness of the structural plane. \(DEV\cong 0\) indicates that the central point and its neighborhood lie within the same plane. The closer the DEV value is to 0, the more distinct the planar feature becomes. Therefore, values 3, 5, and 8 are identified as structural planes. Extract these values and further identify the more prominent and certain structural planes among them, as shown in Figure 8.  
Figure 5: Rock Surface Raster Model. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Cluster Partition** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline DEV & \(\backslash\) & \(\backslash\) & \(-0.0009\) & \(\backslash\) & 0.0001 & \(-0.0017\) & \(-0.0038\) & \(-0.0004\) \\ \hline \end{tabular}
\end{table} 
Table 3: The calculation results of the DEV. Figure 6: (a) Slope, (b) Aspect, (c) Elevation standard deviation, and (d) ISODATA clustering results. Figure 7: Comparison before and after filtering. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Red** & **Dip Direction (\({}^{\circ}\))** & \multicolumn{2}{c}{**Dip Angle**} & \multicolumn{2}{c}{**Space (m)**} & \multicolumn{2}{c}{**Red**} & \multicolumn{2}{c}{**Dip Direction (\({}^{\circ}\))**} & \multicolumn{2}{c}{**Dip Angle (\({}^{\circ}\))**} & \multicolumn{2}{c}{**Space (m)**} \\ \hline
1 & 90.47 & 59.69 & / & 11 & 92.16 & 50.47 & 0.754 \\
2 & 89.55 & 63.62 & 0.035 & 12 & 96.88 & 58.54 & 0.380 \\
3 & 87.92 & 57.87 & 0.004 & 13 & 100.86 & 59.01 & 0.334 \\
4 & 95.80 & 54.56 & 1.152 & 14 & 103.55 & 68.60 & 0.066 \\
5 & 91.33 & 57.09 & 0.278 & 15 & 89.60 & 66.55 & 0.580 \\
6 & 92.39 & 50.63 & 1.042 & 16 & 93.29 & 58.57 & 0.488 \\
7 & 90.55 & 53.66 & 0.028 & 17 & 91.77 & 52.41 & 0.200 \\
8 & 83.70 & 63.06 & 0.156 & 18 & 92.88 & 54.89 & 0.161 \\
9 & 105.99 & 66.68 & 0.156 & 19 & 96.35 & 54.97 & 1.309 \\
10 & 90.95 & 60.39 & 0.049 & 20 & 87.65 & 54.30 & 0.122 \\ \hline \multicolumn{1}{c}{} & \multicolumn{2}{c}{Trace} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & Trace \\ Red & Midpoint Coordinates of Trace (m) & Length & Red & Midpoint Coordinates of Trace (m) & Length (m) \\ \hline
1 & 2.52 & 4.51 & \(-\)2.90 & 0.07 & 11 & 1.39 & 2.54 & \(-\)2.03 & 0.13 \\
2 & 4.77 & 4.34 & \(-\)3.52 & 0.07 & 12 & 2.9  
In the characterization of structural surfaces, due to differences in the model, it is necessary to distinguish between joints, layers, and faults. The sampling window persistence is 5 m \(\times\) 5 m, resulting in a trace line density of 0.8. The inter-group spacing of the joint structural planes is 0.381 m, which is close to 0.4 m, so it is classified into the \"MS1\" category. Using formulas (1), (2), and (3), the calculated volumetric density is 20 structural planes divided by a volume of 75 m\({}^{3}\), resulting in a value of 0.27.