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Abstract The influence of the particle size on the vertical plate penetration into dense cohesionless granular materials was numerically investigated. Simulations were performed in quasi-two-dimensional conditions by changing the mean particle diameters d50 but maintaining the plate thickness B from B/d50 = 63–2.6. The initial bulk packing fraction was kept high, irrespective of the particle size. In the smallest particle size case (B/d50 = 63), the size ratio reached almost the same level as that in the laboratory experiments using natural sand particles. The results demonstrated that the mean penetration resistance force acting on the plate tip surface increases with a decrease of B/d50, while the tangential force acting on the side surfaces does not change with B/d50. Tip resistances increase linearly with the penetration depth, while the tangential resistances increase with the square of the depth regardless of B/d50. The behavior of the resistance fluctuations changes qualitatively between B/d50 = 31 and 21. For all cases, we confirmed the formation of a wedge-shaped flow with a high forward velocity in front of the plate tip. The wedge flow width was larger than the plate thickness by almost a mean particle diameter, and was responsible for the increase in the mean resistance depending on the particle size. For the large B/d50 cases only, the resistance exhibited quasi-periodic fluctuations, which was attributable to the intermittent nucleation and disappearance of the shear bands. Moreover, we investigated the dependence of B/d50 on the band evolutions by analyzing the band thickness. Graphic abstract The influence of the particle size on the vertical plate penetration into dense cohesionless granular materials was numerically investigated using DEM. Simulations were performed in quasi-two-dimensional conditions by changing the median particle diameters d50 but maintaining the plate thickness B. The initial bulk packing fraction was kept high, irrespective of the particle size. Upper and lower figures show the result of small (B/d50 = 63) and large particle size case (B/d50 = 21), respectively. In the small particle size case (B/d50 = 63), the size ratio reached almost the same level as that in the laboratory and the dynamics of 35.5 million particles was considered. Right and left figures illustrate instantaneous shear strain rate and local packing fraction distributions, respectively. Large qualitative change in the granular behaviors as well as penetration resistance was observed between B/d50 = 31 and 21. The intermittent nucleation and disappearance of the shear bands were clearly observed only for large B/d50 cases.

The response of granular materials to plate drag is numerically studied using a large-scale discrete element method (DEM) simulation. The effect of the initial volume fraction of the materials on the drag force acting on the plate is examined. The results show that a volume-fraction-dependent bifurcation occurs in the force; in an initially loose granular bed, the force reaches an approximately constant value as the plate advances, while in an initially dense bed, the force oscillates with a large amplitude. The force oscillation is attributed to the periodic evolution of a shear band formed only in the dense bed. The behaviors of the drag force and shear band, which depend on the initial volume fraction in the DEM simulation, are in close agreement with those obtained experimentally in previous studies [N. Gravish et al., Phys. Rev. Lett. 105, 128301 (2010); Phys. Rev. E 89, 042202 (2014)]. Further analysis using the DEM simulation shows that the formation of the shear band is explained by the local dilation and compaction of the granular materials induced by the plate drag. Independent of the volume fraction, materials dilate in a wedge-shaped flow region that formed in front of the plate. In the loose bed, a compacted front builds up ahead of the flow region. Because the compacted front advances into a weaker undisturbed region, the flow region behind the front can constantly advance. On the other hand, in the dense bed, the materials largely dilate in a disturbed flow region formed in front of the plate. Because a denser undisturbed region is more stable compared to the flow region, the flow region is strongly confined. As a result, the shear strain is localized along a flow boundary between these regions, and the shear band develops.

To improve the energy efficiency of construction and mining machineries such as hydraulic excavator and bulldozer, it is important to optimize the shape of tools, which are used to handle ground materials directly such as buckets and blades, and earthmoving processes. It is impossible without a deep understanding of interactions between mechanical tools and ground materials. In the present study, a DEM model based on multi-sphere approach is developed for the gravel excavation process using a hydraulic excavator bucket. Granular materials in nature include several geometrical factors over different scales and it is computationally expensive to model real particle shapes as they are, especially for practical engineering design problems. It is mandatory to develop a simplified model which only includes essential geometrical factors that are important for gravel-tool interactions. In the present study, the role of particle roundness on digging process is investigated. We find that smaller roundness prevents the rotational motion of particles and strengthens the shear resistance of the layer. In addition, particles with higher angular velocity are localized in a narrow zone where the formation of shear band is expected during digging processes.