Relaxation mechanics of granular slopes by rotation or vibration

The angle of a static granular slope can remain stable up to a specific value known as the angle of repose, which characterizes the bulk frictional properties of the granular material. Although a granular slope with an angle smaller than the angle of repose is statically stable, it can be destabilized by external loading or perturbations. Specifically, granular slopes relax when subjected to rotation or vibration. However, the deformation mechanics under these two conditions may differ. To elucidate the similarities and differences between them, two experimental results on granular rotation and vibration are compared. Regarding the granular rotation, relaxation of a granular heap under the influence of centrifugal force is investigated (Irire et al., PRE 104, 064902 (2021)). The experimental results indicate that surface deformation can be explained by a simple force balance model that incorporates gravity, friction, and centrifugal force. This setup also enables a systematic study of how the angle of repose depends on body forces, such as gravity and centrifugal force. Then, the relaxation dynamics of a vibrated granular dent mimicking a crater shape is investigated. The results reveal that the global trend of the relaxation process can be described by linear diffusive relaxation. By the systematic experiments, the dependence of the diffusion coefficient on various parameters is experimentally evaluated, and a simple form for the diffusion coefficient is obtained. In the rotational case, only a thin surface layer of the granular slope is fluidized, whereas in the vibrational case, fluidization extends into a much thicker region. This difference primarily accounts for the distinct deformation/relaxation behaviors observed under the two conditions.