We present evidence for the interactions between a ball and the container boundaries, as well as between two balls, that are mediated by the granular medium during impact cratering. The presence of the bottom boundary affects the final penetration depth only for low drop heights with shallow filling, in which case, surprisingly, the penetration becomes deeper. By contrast the presence of the side wall causes less penetration and also an effective repulsion. Repulsion is also found for two balls dropped side-by-side.
Sudden release of energy in explosion creates craters in granular media. In comparison with well-studied impact cratering in granular media, our understanding of explosion cratering is still primitive. Here, we study low-energy lab-scale explosion cratering in 3D granular media using controlled pulses of pressurized air. We identify four regimes of explosion cratering at different burial depths, which are associated with distinct explosion dynamics and result in different crater morphologies. We propose a general relation between the dynamics of granular flows and the surface structures of res…
When a granular material is impacted by a sphere, its surface deforms like a liquid yet it preserves a circular crater like a solid. Although the mechanism of granular impact cratering by solid spheres is well explored, our knowledge on granular impact cratering by liquid drops is still very limited. Here, by combining high-speed photography with high-precision laser profilometry, we investigate liquid-drop impact dynamics on granular surface and monitor the morphology of resulting impact craters. Surprisingly, we find that, despite the enormous energy and length difference, granular impact cr…
Combining high-speed photography with laser profilometry, we study the dynamics and the morphology of liquid-drop impact cratering in wet granular media---a ubiquitous phenomenon relevant to many important geological, agricultural, and industrial processes. By systematically investigating important variables such as impact energy, the size of impinging drops and the degree of liquid saturation in granular beds, we uncover a novel scaling for the size of impact craters. We show that this scaling can be explained by considering the balance between the inertia of impinging drops and the strength …
Experiments on the low-speed impact of solid objects into granular media have been used both to mimic geophysical events and to probe the unusual nature of the granular state of matter. Observations have been interpreted in terms of conflicting stopping forces: product of powers of projectile depth and speed; linear in speed; constant, proportional to the initial impact speed; and proportional to depth. This is reminiscent of high-speed ballistics impact in the 19th and 20th centuries, when a plethora of empirical rules were proposed. To make progress, we developed a means to measure projectil…
We present data for the penetration of a variety of spheres, dropped from rest, into a level non-cohesive granular medium. We improve upon our earlier work [Uehara {\it et al.} Phys. Rev. Lett. {\bf 90}, 194301 (2003)] in three regards. First, we explore the behavior vs sphere diameter and density more systematically, by holding one of these parameters constant while varying the other. Second, we prepare the granular medium more reproducibly and, third, we measure the penetration depth more accurately. The new data support our previous conclusion that the penetration depth is proportional to t…
Although a large number of astronomical craters are actually produced by the oblique impacts onto inclined surfaces, most of the laboratory experiments mimicking the impact cratering have been performed by the vertical impact onto a horizontal target surface. In previous studies on the effects of oblique impact and inclined terrain, only one of the impact angle $φ$ or target inclination angle $θ$ has been varied in the experiments. Therefore, we perform impact-cratering experiments by systematically varying both $φ$ and $θ$. A solid projectile of diameter $D_{\rm i}=6$~mm is impacted onto a sa…
The erosion of lunar soil by rocket exhaust plumes is investigated experimentally. This has identified the diffusion-driven flow in the bulk of the sand as an important but previously unrecognized mechanism for erosion dynamics. It has also shown that slow regime cratering is governed by the recirculation of sand in the widening geometry of the crater. Scaling relationships and erosion mechanisms have been characterized in detail for the slow regime. The diffusion-driven flow occurs in both slow and fast regime cratering. Because diffusion-driven flow had been omitted from the lunar erosion th…
We report on the penetration of cylindrical projectiles dropped from rest into a dry, noncohesive granular medium. The cylinder length, diameter, density, and tip shape are all explicitly varied. For deep penetrations, as compared to the cylinder diameter, the data collapse onto a single scaling law that varies as the 1/3 power of the total drop distance, the 1/2 power of cylinder length, and the 1/6 power of cylinder diameter. For shallow penetrations, the projectile shape plays a crucial role with sharper objects penetrating deeper.
Projectile impact into a light granular material composed of expanded polypropylene (EPP) particles is investigated systematically with various impact velocities. Experimentally, the trajectory of an intruder moving inside the granular material is monitored with a recently developed non-invasive microwave radar system. Numerically, discrete element simulations together with coarse-graining techniques are employed to address both dynamics of the intruder and response of the granular bed. Our experimental and numerical results of the intruder dynamics agree with each other quantitatively and are…
The impact of a hydrogel sphere onto a granular target results in both the deformation of the sphere and the formation of a prominent topographic feature known as impact crater on the granular surface. We investigate the crater formation and scaling, together with the spreading diameter and post-impact dynamics of the spheres by performing a series of experiments, varying the Young's modulus $Y$ and impact speed $U_{0}$ of the hydrogel spheres, and the packing fraction and grain size of the granular target. We determine how the crater diameter and depth depend on $Y$ and find the data to be co…
When a solid projectile impacts a granular target, it experiences a drag force and abruptly comes to rest as its momentum transfers to the grains. An empirical drag force law successfully describes the force experienced by the projectile, and the corresponding grain-scale mechanisms have been deciphered for normal impacts. However, there is little work exploring non-normal impacts. Accordingly, we extend studies to explore oblique impact, in which a significant horizontal component of the drag force is present. In our experiments, a projectile impacts a quasi-two-dimensional bed of bidisperse …
Impact dynamics is measured for spherical and cylindrical projectiles of many different densities dropped onto a variety non-cohesive granular media. The results are analyzed in terms of the material-dependent scaling of the inertial and frictional drag contributions to the total stopping force. The inertial drag force scales similar to that in fluids, except that it depends on the internal friction coefficient. The frictional drag force scales as the square-root of the density of granular medium and projectile, and hence cannot be explained by the combination of granular hydrostatic pressure …
How does the impact of a deformable droplet on a granular bed differ from that caused by a solid impactor of similar size and density? Here, we experimentally study this question and focus on the effect of intruder deformability on the crater shape. For comparable impact energies, we show that the crater diameter is larger for droplets than for solid intruders but that the impact of the latter results in deeper craters. Interestingly, for initially dense beds of packing fractions larger than 0.58, we find that the resultant excavated crater volume is independent of the intruder deformability, …
By means of novel volume-diameter aspect ratio diagrams, we ponder on the current conception of crater morphogenesis analyzing crater data from beam explosions, hypervelocity collisions and drop experiments and comparing them with crater data from three moons (the Moon, Callisto, and Ganymede) and from our own experimental results. The distinctive volume-diameter scaling laws we discovered make us to conclude that simple and complex craters in satellites and planets could have been formed by granular vs. granular collisions and that central peaks and domes in complex craters were formed by a d…
Impact of a solid object onto a small-body surface can be modeled by the solid impact onto a hierarchically structured granular target. Impact drag force model for the hierarchically structured granular target is developed based on the experiment. We perform a set of granular impact experiments in which mechanical strength and porosity of target grains are systematically varied. Tiny glass beads ($5$~$μ$m in diameter) are agglomerated to form porous grains of $2$--$4$~mm in diameter. Then, the grains are sintered to control their strength. A polyethylene sphere ($12.7$~mm in diameter) is dropp…
Dynamic characterization of mechanical properties of dust aggregates has been one of the most important problems to quantitatively discuss the dust growth in protoplanetary disks. We experimentally investigate the dynamic properties of dust aggregates by low-speed ($\lesssim 3.2$ m s$^{-1}$) impacts of solid projectiles. Spherical impactors made of glass, steel, or lead are dropped onto a dust aggregate of packing fraction $ϕ=0.35$ under vacuum conditions. The impact results in cratering or fragmentation of the dust aggregate, depending on the impact energy. The crater shape can be approximate…
The impact-induced energy transfer and dissipation in granular targets without any confining walls are studied by microgravity experiments. A solid projectile impacts into a granular target at low impact speed ($0.045 \leq v_p \leq 1.6$~m~s$^{-1}$) in a laboratory drop tower. Granular clusters consisting of soft or hard particles are used as targets. Porous dust agglomerates and glass beads are used for soft and hard particles, respectively. The expansion of the granular target cluster is recorded by a high-speed camera. Using the experimental data, we find that (i)~a simple energy scaling can…
We study the impact of a projectile onto a bed of 3 mm grains immersed in an index-matched fluid. Specifically, we vary the amount of prestrain on the sample, strengthening the force chains within the system. We find this affects only the prefactor of linear depth-dependent term in the stopping force. We therefore attribute this term to pressure within the material, and not the grain-intruder friction as is sometimes suggested. Using a laser sheet scanning technique to visualize internal grain motion, a high-speed camera, and particle tracking, we can measure the trajectory of each grain throu…
We measure the quasi-static friction force acting on intruders moving downwards into a granular medium. By utilizing different intruder geometries, we demonstrate that the force acts locally normal to the intruder surface. By altering the hydrostatic loading of grain contacts by a sub-fluidizing airflow through the bed, we demonstrate that the relevant frictional contacts are loaded by gravity rather than by the motion of the intruder itself. Lastly, by measuring the final penetration depth versus airspeed and using an earlier result for inertial drag, we demonstrate that the same quasi-static…
We present experimental measurements of penetration depths for the impact of spheres into wetted granular media. We observe that the penetration depth in the liquid saturated case scales with projectile density, size, and drop height in a fashion consistent with the scaling observed in the dry case, but that penetration depths into saturated packings tend to be smaller. This result suggests that, for the range of impact energies observed, the stopping force is set by static contact forces between grains within the bed, and that the presence of liquid serves, primarily, to enhance these contact…
We develop an original apparatus of the granular impact experiment by which the incident angle of the solid projectile and inclination angle of the target granular layer can be systematically varied. Whereas most of the natural cratering events occur on inclined surfaces with various incident angles, there have not been any experiments on oblique impacts on an inclined target surface. To perform systematic impact experiments, a novel experimental apparatus has to be developed. Therefore, we build an apparatus for impact experiments where both the incident angle and the inclination angle can be…
The collapse of an inclined cohesive granular layer triggered by a certain perturbation can be a model for not only landslides on Earth but also relaxations of asteroidal surface terrains. To understand such terrain dynamics, we conduct a series of experiments of a solid-projectile impact onto an inclined wet granular layer with various water contents and inclination angles. As a result, we find two types of outcomes: "crater formation" and "collapse". The "collapse" phase is observed when the inclination angle is close to the maximum stable angle and the impact-induced vibration at the bottom…
Penetration of Rigid Rods, Flexible Rods, and Granular Jets into Low-Density Granular Media
Instituto de Física, Benemérita Universidad Autónoma de Puebla（普埃布拉自治大学物理研究所）；Gulliver, CNRS, ESPCI Paris, Université PSL（高勒维尔实验室，法国国家科学研究中心，巴黎高等物理化工学院，巴黎文理研究大学）
Crater Depth Prediction in Granular Collisions: A Uniaxial Compression Model
Universidad Autónoma de San Luis Potosí, Instituto de Física（圣路易斯波托西自治大学物理研究所）；Gran Sasso Science Institute（格兰萨索科学研究所）；Universidad Autónoma de San Luis Potosí, Facultad de Ciencias（圣路易斯波托西自治大学理学院）
For a fundamental understanding of terrain relaxation occurring on sloped surfaces of terrestrial bodies, we analyze the crater shape produced by an impact on an inclined granular (dry-sand) layer. Owing to asymmetric ejecta deposition followed by landsliding, the slope of the impacted inclined surface can be relaxed. Using the experimental results of a solid projectile impact on an inclined dry-sand layer, we measure the distance of centroid migration induced by asymmetric cratering. We find that the centroid migration distance $x_\mathrm{mig}$ normalized to the crater minor-axis diameter $D_…
