Depth dependence of vertical plunging force in granular medium.

Depth dependence of vertical plunging force in granular medium is studied experimentally by measuring the slow-pushing force of different size and shape objects intruding vertically into a granular bed. It is found that all of the force curves of fully immersed intruders have concave-to-convex transition. The depth dependence of the force turns from supralinear to sublinear. By studying the properties of the inflection point of the concave-convex transition, we find that the plunging force at inflection point is proportional to intruder's volume, and the inflection point occurs when the intruder is fully buried to a level around twice its diameter. Testing by plunging a long cylinder, which is always partially immersed, we find no inflection point in this case, which verifies that the inflection of the plunging force is related to the filled-in loose granules on top of the intruder. The slowdown of the increasing rate of the force is, therefore, not a result of sidewall support proposed by previous researchers.