# Laboratory experiment and discrete-element-method simulation of granular-heap flows under vertical vibration

## TL;DR

This study combines laboratory experiments and discrete-element-method simulations to analyze granular heap flows under vertical vibration, confirming the applicability of a nonlinear diffusion transport model and revealing the shear band structure's characteristics.

## Contribution

It demonstrates that a nonlinear diffusion transport model accurately describes surface velocities and internal flow profiles in vibrated granular heaps, supported by both experiments and simulations.

## Key findings

- Velocity decreases exponentially with depth from the surface.
- Shear band thickness scales with local pile height.
- Flow profile integration matches the nonlinear diffusion model.

## Abstract

Granular flow dynamics on a vertically vibrated pile is studied by means of both laboratory experiments and numerical simulations. As already revealed, the depth-averaged velocity of a fully-fluidized granular pile under strong vibration, which is measured by a high-speed laser profiler in the experiment, can be explained by the nonlinear diffusion transport model proposed by our previous paper (Tsuji et al, Phys. Rev. Lett. 120, 128001 (2018)). In this paper, we report that a similar transport model can be applied to the relation between the surface velocity and slope in the experiment. These facts are also reproduced by particle-scale numerical simulations based on the discrete element method. In addition, using these numerical results, the velocity profile inside the fluidized pile is measured. As a result, we show that the flow velocity decreases exponentially with depth from the surface of the pile, which means that a clearly fluidized region, also known as shear band structure, is localized around the surface. However, its thickness grows proportionally with the local height of the pile, i.e., the shear band does not consist of a fluidized layer with a constant thickness. From these features, we finally demonstrate that the integration of this exponentially-decreasing velocity profile is consistent with the depth-averaged velocity predicted by the nonlinear diffusion transport model.