Penetration depth scaling for impact into wet granular packings

Drag force regime in dry and immersed granular media

The drag force acting on an intruder colliding with granular media is typically influenced by the impact velocity and the penetrating depth. In this paper, the investigation was extended to the dry and immersed scenarios through coupled simulations at different penetrating velocities. The drag force regime was clarified to exhibit velocity dependence in the initial contact stage, followed by the inertial transit stage with a F∼z^{2} (force-depth) relationship. Subsequently, it transitioned into the depth-dependent regime in both dry and immersed cases. The underlying rheological mechanism was explored, revealing that, in both dry and immersed scenarios, the granular bulk underwent a state relaxation process, as indicated by the granular inertial number. Additionally, the presence of the ambient fluid restricted the flow dynamics of the perturbed granular material, exhibiting a similar rheology as observed in the dry case.

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.

Penetration in bimodal, polydisperse granular material

We investigate the impact penetration of spheres into granular media which are compositions of two discrete size ranges, thus creating a polydisperse bimodal material. We examine the penetration depth as a function of the composition (volume fractions of the respective sizes) and impact speed. Penetration depths were found to vary between δ=0.5D_{0} and δ=7D_{0}, which, for mono-modal media only, could be correlated in terms of the total drop height, H=h+δ, as in previous studies, by incorporating correction factors for the packing fraction. Bimodal data can only be collapsed by deriving a critical packing fraction for each mass fraction. The data for the mixed grains exhibit a surprising lubricating effect, which was most significant when the finest grains [d_{s}∼O(30) μm] were added to the larger particles [d_{l}∼O(200-500) μm], with a size ratio, ε=d_{l}/d_{s}, larger than 3 and mass fractions over 25%, despite the increased packing fraction. We postulate that the small grains get between the large grains and reduce their intergrain friction, only when their mass fraction is sufficiently large to prevent them from simply rattling in the voids between the large particles. This is supported by our experimental observations of the largest lubrication effect produced by adding small glass beads to a bed of large sand particles with rough surfaces.