Local stresses in the Janssen granular column

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}∝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 quasistatic 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.

Silo collapse under granular discharge

We investigate, at a laboratory scale, the collapse of cylindrical shells of radius R and thickness t induced by a granular discharge. We measure the critical filling height for which the structure fails upon discharge. We observe that the silos sustain filling heights significantly above an estimation obtained by coupling standard shell-buckling and granular stress distribution theories. Two effects contribute to stabilize the structure: (i) below the critical filling height, a dynamical stabilization due to granular wall friction prevents the localized shell-buckling modes to grow irreversibly; (ii) above the critical filling height, collapse occurs before the downward sliding motion of the whole granular column sets in, such that only a partial friction mobilization is at play. However, we notice also that the critical filling height is reduced as the grain size d increases. The importance of grain size contribution is controlled by the ratio d/√[Rt]. We rationalize these antagonist effects with a novel fluid-structure theory both accounting for the actual status of granular friction at the wall and the inherent shell imperfections mediated by the grains. This theory yields new scaling predictions which are compared with the experimental results.