Fuzzy partitioning algorithms applied to the interpretation of distinct element modelling results

The distinct element method (DEM) has emerged as one of the principal computational methods for problems involving the analysis of fractured rock masses. The DEM is a recursive, time-stepping technique, and complex models may take many hundreds of thousands of cycles to converge to equilibrium. Even with fast computers this can be time consuming, and—depending on the model under consideration—may be strictly unnecessary, as the instability of the model is clear. Here, we demonstrate how the fuzzy c means (FCM) clustering algorithm can be used to analyse the kinematic and dynamic behaviour of the material in a DEM model. Clustering based on kinematics allows blocks to be interpreted in terms of the form of their instability (i.e. falling, sliding or stable), and clustering based on dynamics (i.e. forces and moments) can be used to delineate the zone of unstable rock around an excavation. Determination of the size of the zone of unstable rock leads directly to a calculation of support pressure.