Strain Localization During the Transition Region and Critical State in Granular Materials

Understanding strain localization in granular materials, particularly during the transition region and the critical state, is crucial for predicting failure in geophysical phenomena such as landslides and earthquakes, and for improving soil constitutive models. In this study, the transition region is defined as the phase following the elastic region but preceding the critical state, where significant changes in particle interactions and mechanical behavior occur. We conducted triaxial tests on granular materials to investigate strain localization both during the transition region and in the critical state. Using X-ray computed tomography and X-ray diffraction, we collected kinematic and kinetic data, focusing on the relationship between non-affine particle motion and inter-particle force fluctuations under small and large incremental strains. Non-affine motion was quantified using the D²_min metric, and inter-particle forces were inferred from the average stress on individual particles. Additionally, the effect of particle fragmentation on rearrangement and strain localization was examined. We hypothesize that there is a strong correlation between non-affine particle motion and inter-particle force fluctuations, as observed in our previous discrete element method simulations in 2D plane shear tests. Moreover, we suggest that significant particle fragmentation alters the particle size distribution, which reduces the occurrence of stick-slip events within the strain localization band. This hypothesis will be tested by identifying clusters of particles with high D²_min values during both the transition and critical state phases.