Intrusion into Granular Media Beyond the Quasistatic Regime

Anomalous descent of intruders in vibrated gas-fluidized granular materials

The descent of dense intruder disks through granular material fluidized by vertical gas flow and vibration is investigated experimentally and computationally. Single intruders descend with a velocity which oscillates based on distance above the bottom of the system, which simulations show is due to a spatially dependent void fraction in the granular material changing the effective drag force on the intruder. Two vertically aligned intruders undergo a drafting-kissing-tumbling analog which forms because the bottom intruder decelerates due to particle compaction from the weight of the top intruder.

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.

Successive reintrusions in a granular medium

We measure and analyze the drag force experienced by a rigid rod that penetrates vertically into a granular medium and partially withdraws before sinking again. The drag during the successive reintrusions is observed to be significantly smaller than the force experienced in the first run. Two force regimes are evidenced depending on how the reintrusion depth compares with the withdrawal distance Δ. These two regimes are characterized by a force curve of positive and negative curvature and are separated by an inflection point, which is characterized experimentally. We approach the difference between the first intrusion and the following reintrusions by considering a modification in the stress field of the granular material after the partial extraction of the rod. A theoretical model for the stress modification is proposed and allows to rationalize all the experiments realized for different withdrawal distances Δ. This framework introduces a crossover length λ above which the stress modification in the granular medium is maintained and that is shown to depend linearly on Δ. Finally, the model provides a prediction for the location of the inflection points in reasonable agreement with observations.

Effect of two parallel intruders on total work during granular penetrations

The intrusion of single passive intruders into granular particles has been studied in detail. However, the intrusion force produced by multiple intruders separated at a distance from one another, and hence the effect of their presence in close proximity to one another, is less explored. Here, we used numerical simulations and laboratory experiments to study the force response of two parallel rods intruding vertically into granular media while varying the gap spacing between them. We also explored the effect of variations in friction, intruder size, and particle size on the force response. The total work (W) of the two rods over the depth of intrusion was measured, and the instantaneous velocities of particles over the duration of intrusion were calculated by simulations. We found that the total work done by the intruders changes with distance between them. We observed a peak in W at a gap spacing of ∼3 particle diameters, which was up to 25% greater than W at large separation (>11 particle diameters), beyond which the total work plateaued. This peak was likely due to reduced particle flow between intruders as we found a larger number of strong forces-identified as force chains-in the particle domain at gaps surrounding the peak force. Although higher friction caused greater force generation during intrusion, the gap spacing between the intruders at which the peak total work was generated remained unchanged. Larger intruder sizes resulted in greater total work with the peak in W occurring at slightly larger intruder separations. Taken together, our results show that peak total work done by two parallel intruders remained within a narrow range, remaining robust to most other tested parameters.

Efficacy of simple continuum models for diverse granular intrusions

Granular intrusion is commonly observed in natural and human-made settings. Unlike typical solids and fluids, granular media can simultaneously display fluid-like and solid-like characteristics in a variety of intrusion scenarios. This multi-phase behavior increases the difficulty of accurately modeling these and other yielding (or flowable) materials. Micro-scale modeling methods, such as DEM (Discrete Element Method), capture this behavior by modeling the media at the grain scale, but there is often interest in the macro-scale characterizations of such systems. We examine the efficacy of a macro-scale continuum approach in modeling and understanding the physics of various macroscopic phenomena in a variety of granular intrusion cases using two basic frictional yielding constitutive models. We compare predicted granular force response and material flow to experimental data in four quasi-2D intrusion cases: (1) depth-dependent force response in horizontal submerged-intruder motion; (2) separation-dependent drag variation in parallel-plate vertical-intrusion; (3) initial-density-dependent drag fluctuations in free surface plowing, and (4) flow zone development during vertical plate intrusions in under-compacted granular media. Our continuum modeling approach captures the flow process and drag forces while providing key meso- and macro-scopic insights. The modeling results are then compared to experimental data. Our study highlights how continuum modeling approaches provide an alternative for efficient modeling as well as a conceptual understanding of various granular intrusion phenomena.