History-dependent deformation of a rotated granular pile governed by granular friction

Abstract

• Deformation of a rotated granular heap was experimentally measured and modeled by a simple force-balance model. • Hysteresis of the deformation was observed. • Empirical relations between granular friction, centrifugal loading, and packing fraction were obtained. We experimentally examined the history dependence of the rotation-induced granular deformation. As an initial state, we prepared a quasi-two-dimensional granular pile whose apex is at the rotational axis and its initial inclination is at the angle of repose. The rotation rate was increased from 0 to 620 (rpm) and then decreased back to 0. During the rotation, deformation of the rotated granular pile was captured by a camera. From the acquired image data, granular friction coefficient μ was measured as a function of the ratio between centrifugal force and gravity, Γ . To systematically evaluate the variation of μ both in the increasing (spinning up) and decreasing (spinning down) rotation-rate regimes, surface profiles of the deformed granular piles were fitted to a model considering the force balance among gravity, friction, and centrifugal force at the surface. We found that μ value grows in the increasing Γ regime. However, when Γ was reduced, μ cannot recover its initial value. A part of the history-dependent behaviors of the rotated granular pile can be understood by the force balance model.