A spectral method for clustering of rock discontinuity sets

We demonstrate the use of a spectral clustering algorithm as a novel approach for the identification of rock discontinuity sets based on discontinuity orientations. We use the spectral clustering approach with a simple measure of similarity between normal unit vectors in spherical space that is specific to the clustering of rock discontinuity orientations. The performance of the algorithm is studied using benchmark test cases with data sets corresponding to real rock masses. The results show that the algorithm provides good clustering results, providing partitions that agree well with the results of several other clustering algorithms that are commonly used in rock engineering. Furthermore, we show an example case with data sets of discontinuity orientation compiled from the literature, in which the spectral clustering algorithm provides more natural partitions than the other algorithms considered. Additional advantages of the algorithm are that convergence is fast, and that it can be easily (and efficiently) implemented using popular software packages for numerical analysis.