Discontinuity surface orientation extraction and cluster analysis based on point cloud data

Measurement of the orientation of discontinuity surfaces such as joints, fractures, and faults in rock masses is an essential part of research in the fields of geotechnical engineering. This paper proposes a method for extracting rock discontinuity surfaces by combining several algorithms. First, the unit normal vector information of the points in the point cloud is determined using the K-dimension tree (K-d tree) process. Next, the OPTICS algorithm filters out the discontinuity surface sets and the discontinuity surfaces within each set. Finally, Fuzzy C-Means (FCM) is employed to determine the cluster center orientations of the selected discontinuity surface sets and the orientations of the individual discontinuity surfaces. To validate the effectiveness of our method, we use two publicly available standard geometric point cloud models to extract the orientations of the structural surfaces. Then, we also use an actual rock outcrop to further validate the reliability of the method in extracting joint surface sets. The method covers most of the point cloud information and improves the accuracy of the measurements compared to our previous findings. This paper provides an alternative method for extracting discontinuity surfaces and determining the orientation in real projects.