Fuzzy cluster algorithm for the automatic identification of joint sets

Abstract

The task of identifying and isolating joint sets or subgroups of discontinuities existing in data collected from joint surveys is not a trivial issue and is fundamental to rock engineering design. Traditional methods for carrying out the task have been mostly based on the analysis of plots of the discontinuity orientations or their clustering. However, they suffer from their inability to incorporate the extra data columns collected and also lack in objectivity. This paper proposes a fuzzy K-means algorithm, which has the capability of using the extra information on discontinuities, as well as their orientations in exploratory data analysis. Apart from taking into account the hybrid nature of the information gathered on joints (orientation and non-orientation information), the new algorithm also makes no a priori assumptions as to the number of joint sets available. It provides validity indices (performance measures) for assessing the optimal delineation of the data set into fracture subgroups. The proposed algorithm was tested on two simulated data sets in the paper. In the first example, the data set demanded the analysis of discontinuity orientation only, and the algorithm identified both the number of joint sets present and their proper partitioning. In the second example, additional information on joint roughness was necessary to recover the true structure of the data set. The algorithm was able to converge on the correct solution when the extra information was included in the analysis.