An investigation of forces on intruder in a granular material under vertical vibration

By vertically placing a rod in a granular bed consisting of small glass beads under a vertical sinusoidal vibration, the vertical force on the rod is equal to its weight when the rod stays at the equilibrium height. By changing the rodʹs weight, the relationship between the force and the equilibrium height (Frod ~ h) is measured, which shows an inflection point. The inflection point divides the bed into two zones — zone (I) where Frod increases along the bed depth and zone (II) where Frod decreases along the bed depth. The force on a completely immersed sphere, which is calculated based on the force on the rod, is not monotonic along the bed height and has the greatest value (Fmax) at the inflection point. When the sphereʹs weight is smaller than Fmax, the vertical force on the sphere is equal to its weight at two positions along the bed height. The rising/sinking of the sphere is affected by its initial position and density, and the vibration strength.