The influence of gravity on granular impacts

II. A gravity-scaled collision model for slow interactions

¹ Institut Supérieur de l’Aéronautique et de l’Espace, Ave Edouard Belin, 31400 Toulouse cedex 4, France
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² Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice cedex 4, France
³ Centre National d’Études Spatiales, Ave Edouard Belin, 31400 Toulouse cedex 4, France

Received: 27 August 2021
Accepted: 24 November 2021

Abstract

Context. Slow interactions on small body surfaces occur both naturally and through human intervention. The resettling of grains and boulders following a cratering event, as well as observations made during small body missions, can provide clues regarding the material properties and the physical evolution of a surface. In order to analyze such events, it is necessary to understand how gravity influences granular behavior.

Aims. In this work, we study slow impacts into granular materials for different collision velocities and gravity levels. Our objectives are to develop a model that describes the penetration depth in terms of the dimensionless Froude number and to use this model to understand the relationship between collision behavior, collision velocity, and gravity.

Methods. We used the soft-sphere discrete element method to simulate impacts into glass beads under gravitational accelerations ranging from 9.81 m s⁻² to 0.001 m s⁻². We quantified collision behavior using the peak acceleration, the penetration depth, and the collision duration of the projectile, and we compared the collision behavior for impacts within a Froude number range of 0–10.

Results. The measured penetration depth and collision duration for low-velocity collisions are comparable when the impact parameters are scaled by the Froude number, and the presented model predicts the collision behavior well within the tested Froude number range. If the impact Froude number is low (0 < Fr < 1.5), the collision occurs in a regime that is dominated by a depth-dependent quasi-static friction force. If the impact Froude number is high enough (1.5 < Fr < 10), the collision enters a second regime that is dominated by inertial drag.

Conclusions. The presented collision model can be used to constrain the properties of a granular surface material using the penetration depth measurement from a single impact event. If the projectile size, the collision velocity, the gravity level, and the final penetration depth are known and if the material density is estimated, then the internal friction angle of the material can be deduced.