Depth-dependent resistance of granular media to vertical penetration

TL;DR

This study investigates the local frictional forces acting on objects penetrating granular media, revealing how these forces depend on gravity, intruder shape, and impact conditions, with implications for understanding granular resistance.

Contribution

It demonstrates that the quasi-static friction force in granular media is locally normal to the surface, load-dependent on gravity, and consistent during impact, with a universal proportionality constant.

Findings

Friction acts locally normal to intruder surface.

Frictional contacts are loaded by gravity, not intruder motion.

The same friction force applies during impact, with a universal constant.

Abstract

We measure the quasi-static friction force acting on intruders moving downwards into a granular medium. By utilizing different intruder geometries, we demonstrate that the force acts locally normal to the intruder surface. By altering the hydrostatic loading of grain contacts by a sub-fluidizing airflow through the bed, we demonstrate that the relevant frictional contacts are loaded by gravity rather than by the motion of the intruder itself. Lastly, by measuring the final penetration depth versus airspeed and using an earlier result for inertial drag, we demonstrate that the same quasi-static friction force acts during impact. Altogether this force is set by a friction coefficient, hydrostatic pressure, projectile size and shape, and a dimensionless proportionality constant. The latter is the same in nearly all experiments, and is surprisingly greater than one.