Dynamics of an intruder moving through a confined granular medium: Rescaled packing fraction yields data collapse for different intruder and system sizes.

We consider an intruder dragged by a spring though a layer of bidisperse disks constrained in a fixed volume Couette cell in both discrete element simulations and experiments. The spring is loaded slowly, leading to stick-slip dynamics of the intruder. As the intruder advances, the medium develops large density heterogeneities, with a region in front of the intruder more densely packed and a region behind the intruder depleted of particles. We explore a range of annulus widths W, intruder sizes D, and global packing fractions Φ and measure the fluctuating force on the intruder. We find that an effective packing fraction, defined as Φ_eff = Φ W / (W - D), can account for the combined effect of the three variables, collapsing the data to a single curve. When Φ_eff is equal to the steady-state packing fraction of quasi-statically sheared packings under fixed confining pressure, the disks pack after some time into annular regions outside the intruder's path, leaving a channel that allows for unimpeded motion of the intruder. Increasing values of Φ_eff lead to increasing average forces and longer sticking periods as the intruder finds difficult to clear an open channel through which to move.