Penetrating a granular medium by successive impacts

We consider the penetration dynamics of a vertical cylinder into a dry granular medium subjected to successive impacts. The depth of the impactor below the free surface $z_N$ first evolves linearly with the impact number $N$ and then follows a power-law evolution $z_N \propto N^{1/3}$. The depth reached by the cylinder after a given number of impacts is observed to increase with the impact energy but to decrease with its diameter and the density of the granular medium. We develop a model that accounts for the quasi-static and inertial granular forces applying on the cylinder to rationalize our observations. This approach reveals the existence of two intrusion regimes for large and small impact numbers, allowing all data to be rescaled on a master curve. Then, we extend the study to the effect of sidewalls on the dynamics of the impactor. We show that lateral confinement changes the dependence of the impactor depth on the impact number $z_N (N)$. This effect is accounted for by considering the increase of the granular drag with the lateral confinement.