A fast automatic extraction method for rock mass discontinuity orientation using fast k-means++ and fast silhouette based on 3D point cloud

Abstract

In this paper, a fast automatic extraction method for rock discontinuity orientation using fast k-means++ and fast silhouette based on three-dimensional (3D) point cloud is proposed. The main contributions of the proposed method include: (1) a concept of base vector is proposed, (2) a fast k-means++ algorithm and a fast clustering validity index of silhouette are proposed and combined to automatically achieve a fast optimal grouping of discontinuities, and (3) the generation and optimization of independent discontinuity based on a double-clustering algorithm. The proposed method consists of three steps : (1) point cloud preprocessing, (2) optimal grouping of discontinuities, and (3) discontinuity generation and optimization. Several cases, including two polyhedral models under laboratory conditions and two rock slope models, are adopted to verify the accuracy and efficiency of the proposed method. A sensitivity analysis is performed to determine the optimal parameters. The results show that the proposed method can automatically achieve a fast and effective extraction of discontinuity orientations compared with the classical method, Slob (2010), Riquelme et al. (2014) and Li et al. (2016), and the efficiency is significantly improved compared with Rousseeuw (1987), Arthur and vassilvitskii (2007) and Li et al. (2016).