Successive reintrusions in a granular medium

We measure and analyze the drag force experienced by a rigid rod that penetrates vertically into a granular medium and partially withdraws before sinking again. The drag during the successive reintrusions is observed to be significantly smaller than the force experienced in the first run. Two force regimes are evidenced depending on how the reintrusion depth compares with the withdrawal distance Δ. These two regimes are characterized by a force curve of positive and negative curvature and are separated by an inflection point, which is characterized experimentally. We approach the difference between the first intrusion and the following reintrusions by considering a modification in the stress field of the granular material after the partial extraction of the rod. A theoretical model for the stress modification is proposed and allows to rationalize all the experiments realized for different withdrawal distances Δ. This framework introduces a crossover length λ above which the stress modification in the granular medium is maintained and that is shown to depend linearly on Δ. Finally, the model provides a prediction for the location of the inflection points in reasonable agreement with observations.