On the submerging of a spherical intruder into granular beds

Granular materials are complex systems and their mechanical behaviours are determined by the material properties of individual particles, the interaction between particles and the surrounding media, which are still incompletely understood. Using an advanced discrete element method (DEM), we simulate the submerging process of a spherical projectile (an intruder) into granular materials of various properties with a zero penetration velocity (i.e. the intruder is touching the top surface of the granular bed and released from stationary) and examine its settling behaviour. By systematically changing the density and size of the intruder and the particle density (i.e. the density of the particles in the granular bed), we find that the intruder can sink deep into the granular bed even with a zero penetration velocity. Furthermore, we confirm that under certain conditions the granular bed can behave like a Newtonian liquid and the submerging intruder can reach a constant velocity, i.e. the terminal velocity, identical to the settling of a sphere in a liquid, as observed experimentally. A mathematical model is also developed to predict the maximum penetration depth of the intruder. The model predictions are compared with experimental data reported in the literature,good agreement was obtained, demonstrating the model can accurately predict the submerging behaviour of the intruder in the granular media.