Distinguishing and predicting granular failure via multiscale evolution of contact cycle topologies

We examine the spatial evolution of 3-cycle topologies in the contact networks of 2D and 3D granular media under load experiencing one of two modes of failure at the macroscopic scale: diffused or localised. These mesoscale structures encapsulate kinematical signatures of plastic deformation and thus their destruction or deaths provides a means of tracking or predicting macroscopic failure. A multiscale point pattern analysis quantifies the extent of spatial clustering of these structures within the material throughout loading. In samples undergoing failure through strain localisation, 3-cycle deaths exhibit evidence for spatial clustering well before peak shear stress and shear band nucleation. Detection occurs earlier in the loading history compared to more traditional soil mechanics measures, e. g., porosity maps and particle rotations. Moreover the region of strain localisation is delineated by the spatial distribution of the dying 3-cycle contact topologies. In samples undergoing diffuse failure, no evidence of localisation is detected over short strain intervals suggesting an optimal window size to capture key kinematics, with an aim towards using the spatial behaviour of mesoscopic 3-cycles as a tool to classify macroscopic failure modes.