# Dominant Partitioning of Discontinuities of Rock Masses Based on DBSCAN Algorithm
## 1 Introduction  
The widely distributed discontinuous structural planes in rock masses cause the rock masses to have strong discontinuity, heterogeneity and anisotropy [1, 2]. The randomness and uncertainty of rock discontinuities will affect their deformation, strength, permeability, stress-strain behavior and failure mode [3, 4]. The discontinuities of rock masses in natural states have the characteristics of grouping. The grouping of random discontinuities is the basis of characterizing the distribution law of discontinuities, and it is also a prerequisite for the calculation and simulation of random jointed rock mass and the evaluation of rock mass stability. The analysis results have very important practical significance for the selection of rock mass strength parameters, the study of mechanical properties and the evaluation of engineering stability [5, 6, 7, 8, 9]. Engineers try to delineate discontinuities into subsets based on similar orientations when interpreting discontinuity data. Grouping discontinuities with the same or similar properties into the same group is an effective method for statistical analysis of rock discontinuities. This process is also called dominant grouping. When studying the orientations of discontinuities, they are usually projected onto the Schmidt equal-area projection map so that the distribution of the poles of the discontinuities can be observed. On the basis of this projection technique, [PERSON] [10] proposed a counting method to group the discontinuities of rock masses. The method is to draw the contour map of the pole distribution by calculating the number of poles falling into a certain size of the reference circle, and then group the discontinuities according to the shape of the contour map. This method has the advantages of simplicity and practicality. However, it has certain subjectivity, and the grouping results are affected by experience. [PERSON] and [PERSON] [11] used the objective function to overcome the subjectivity of the artificial grouping of the counting method and further optimized the counting method. Based on the counting method, [PERSON] and [PERSON] [12] proposed a critical criterion based on random tests derived from the Poisson distribution to group the discontinuity dominance. [PERSON] et al. [13] improved [PERSON] and [PERSON]'s method. However, the counting method depends largely on the pole density. In addition, the sampling deviation and the size of the reference circle will also affect the classification results [14; 15]. The existence of these problems has promoted geologists to constantly find methods that can spontaneously group the advantages of rock mass discontinuities. Given that the clustering algorithm just meets the needs of this aspect, it is widely used in the dominant grouping of rock mass discontinuities. Based on fuzzy theory, [PERSON] [16] first used the traditional fuzzy K-means clustering algorithm to study the grouping characteristics of rock mass discontinuities. However, given that the occurrence of discontinuities is a spherical parameter (usually represented by dip direction and dip angle), this method has defects in processing spherical data. Later, [PERSON] and [PERSON] [17] improved the fuzzy K-means algorithm so that the method can be well applied to deal with spherical data. Considering that the classification results of the fuzzy K-means algorithm are largely affected by the distance measure, [PERSON] and [PERSON] [18] have conducted in-depth discussions on the selection of distance measures. However, this method is a local search optimization method and the calculation results are greatly affected by the initial clustering center. More recently, [PERSON] and [PERSON] [19] used four dominant grouping methods for a comparative study, including the nearest neighbor algorithm, K-means algorithm, fuzzy theory and vector digitization method. [PERSON] and [PERSON] [20] proposed a spectral clustering algorithm for the occurrence of discontinuities in rock masses.