Unified penetration depth of low-velocity intruders into granular packings.

Penetration of intruders into granular packings is well described by separately considering the dry or wet case of granular environments in previous experiments and simulations; however, the unified description of such penetration depth in these two granular media remains elusive due to lacking clear explanations about its origins. Based on three-dimensional discrete element method simulations, we introduce a power-law fitting form of the final penetration depth of a spherical intruder with low velocity vertically penetrating into dry and wet granular packings, excellently expressed on a master curve as a power-law function of a dimensionless impact number that is defined as the square root of the ratio between the inertial stress of the intruder and the linear combination of the mean gravitational stress and the cohesive stress exerted on each grain in the packings, as a remarkable extension of the inertial number in dry granular flows. This scaling robustly provides physical insights inherent in the unified description of the material properties of granular packings and the impactor penetration conditions on the final penetration depth in the impact tests, providing evidence of impact properties in different disciplines and applications in science and engineering.