Finite-Size Effects in Geophysical Granular Flow from a Nonlocal Rheology Perspective

Geophysical granular flow is ubiquitous in nature and plays a crucial role in shaping the landscape (hillslope creep, riverbed evolution) and causing geohazards (landslide, debris flow). Small-scale models are an effective way to understand these natural phenomena at large scales. However, finite-size effects inevitably occur due to the multi-scale nature of granular materials, hindering integration of mechanisms obtained from small-scale investigations and continuum models (e.g., granular flow rheology) for large-scale applications. Here we use granular column collapse as a model case to address finite-size effects in granular flows from a novel rheological perspective. We computationally simulate column collapse of varying system-to-particle size ratios using the discrete element method and extract detailed local rheological information during the flow via a coarse-graining technique. We find a disproportional increase in the dimensionless runout distance with the system-to-grain size ratio and a significant difference in the dynamic process. This discrepancy is reflected in the μ(I) curve as non-collapsed data at low inertial number regimes, but casting the data into a non-local rheology framework proposed by Kim and Kamrin (2020) leads to data collapse onto a single master curve for all simulations. This indicates that the finite-size effect is controlled by velocity fluctuations at the grain scale and is a manifestation of the non-locality of granular materials. As a result, the introduction of an intermediate length scale that reflects velocity fluctuations is expected to enable accurate modeling of geophysical granular flows with varying system and particle sizes in a unified continuum framework. It also provides a new perspective for continuum modeling of polydispersity, size segregation, hysteresis, and other size-dependent phenomena in geophysical granular systems.