# Dominant Partitioning of Discontinuities of Rock Masses Based on DBSCAN Algorithm
## 3 Example Analyses
### Application to a Real Data Set  
Maji Hydropower Station is located in Muijiaia Village, Maji Township, Fugong County, Yunnan Province. The dam site area belongs to a deep canyon landform and the valley shape is a 'V' type (Figure 6). The C2 line is proposed to be the layout line of the concrete double-curvature arch dam. The design dam height is 300 m, the installed capacity is 4200 MW, the normal storage level is 1570 m and the average annual power generation is 189.7 \(\times\) 108 kW\(\cdot\)h, which is a world-class high dam.  
The data of this study were obtained from the random discontinuity of the adit PD274 survey. The adit of PD274 is located at the elevation of 1450 m on the right abutment of Maji Hydropower Station on Nujiang River (Figure 7). The direction of the adit is about 280\({}^{\circ}\), roughly perpendicular to the direction of the river. The adit is about 200 m long and about 2 m high and wide. The exposed lithology in the adit is mainly mixed granite and mixed gneiss, with a small amount of white granite dyke development. A total of 294 random discontinuities were measured in this adit by using the window survey sampling method. Figure 8 is a two-dimensional trace diagram of adit PD274. The equal area upper hemisphere pole diagram of the random discontinuity surface of the adit has been drawn, as shown in Figure 9. It can be seen from Figure 8 that the discontinuities of PD274 can be roughly divided into four groups, two groups of steep dip angles and two groups of gentle dip angles.  
Figure 6: Geomorphology and geology of the dam site.  
Figure 8: Two-dimensional trace of discontinuous surface of downstream wall of PD274.  
Figure 7: Location of adits.  
Figure 9: PD274 of discontinuous surface equal area upper hemisphere pole figure.  
shortcoming of the fuzzy C-means clustering analysis method is that it is sensitive to noise and outliers, which has not been effectively solved. The density-based spatial clustering of applications with noise (DBSCAN) algorithm starts from sample density and connects samples through the clustering results, which has the function of filtering noise and isolated values. This paper presents a K-means algorithm based on the DBSCAN algorithm for the identification of discontinuity sets based on orientations.  
In the new method, the acute angle between the normal vectors of the discontinuity elements is selected as the distance measure, and the center of the discontinuous surface set is calculated using the feature analysis method. For the example of an artificial data set, the new method performed well in identifying discontinuous point sets, and the partitions provided were very consistent with the predefined natural clustering. By comparing with the clustering results of K-means algorithm, an improvement is shown. We analyzed the results of each method of clustering the poles on the boundary between clusters to determine whether these poles were assigned to their nearest clusters. The results show that the performance of the new method was slightly better than the other three methods in successfully assigning the structural plane to its nearest neighbor.