Packing-dependent granular friction exerted on a rod withdrawn from a granular layer: the role of shear jamming

Resistance force acting on a rod vertically withdrawn from a granular layer is studied by experiments and numerical simulations. The initial packing fraction of the granular layer is controlled to evaluate the packing dependence of the resistance force. In both experiments and numerical simulations, the frictional resistance force in the steady slipping regime increases as the initial packing fraction is increased. According to the numerical results, the principal reason for the increase of frictional resistance is the increase of normal force acting on the rod. This large normal force stems from the effective solidification of the granular layer which is caused by the shearing induced by the withdrawn rod. Based on this shear-induced solidification, the experimental data are analyzed using a simple 'cylindrical shear-jammed zone' model. Then, the critical divergence of the size of solidified (shear-jammed) zone is observed by increasing the initial packing fraction towards the jamming packing fraction.