Collapse of a rectangular well in a quasi-two-dimensional granular bed

Abstract

We report on an experimental and numerical study of the collapse under gravity of a rectangular well in a quasi-two-dimensional granular bed. For comparison, we also perform experiments on the collapse of a single vertical step. Experiments are conducted in a vertical Hele-Shaw cell, which allows the flow to be recorded from the side using high-speed video. If the rectangular well is sufficiently narrow, the collapsing sidewalls collide at the center of the well and the dynamics of the collapse are dependant on the aspect ratio of the initial well. We follow the evolution of the free surface from the video images, and use particle image velocimetry to determine the subsurface velocity field. From these data, the potential and kinetic energy of the system are calculated. We observe two stages to the collapse flow: an initial gravity-dominated stage, during which the kinetic energy increases, and a later dissipation-dominated phase during which the kinetic energy decreases. We find that although both the width and depth of the depression that remains after the well has collapsed depend on the initial aspect ratio, the surface profiles are self-similar; that is, the shape of the final profile is independent of the aspect ratio of the initial well. We model the collapse of the well using a depth-averaged continuum model with basal friction and with a discrete element model. Both models give results which agree well with experiment. The discrete element model indicates that friction between the particles is the most important source of dissipation over the course of the collapse.

Simulations of granular gravitational collapse

“…When a granular gas evolves freely in gravity without additional energy input, inelastic collisions cool the gas and freeze it into a granular solid in a finite time [1,2]. The role gravity plays in the transition from collision-dominated dynamics to multiple contact dynamics is well researched in some density regimes, as in granular impact craters [3,4] or the transient flow after failure of a granular step [5,6]. Yet the inelastic collapse of a granular gas under gravity, or granular gravitational collapse, is not nearly as well understood as these or related granular gas phenomena, such as the inelastic collapse of a gas evolving without gravity [7] or the energy decay in the homogeneous cooling state [8][9][10].…”

Craters and Granular Jets Generated by Underground Cavity Collapse

“…Low speed impact experiments on granular materials have been an alternative to studying the fundamentals of impact cratering [14][15][16][17][18][19]; it is believed that the shape of a planetary crater is determined by the collapse of an unstable cavity excavated by the meteorite [4], and it has been assumed that a similar process is at work in the case of low-energy impacts on a granular bed. In that regard, and to avoid the complications introduced by the impact itself, the crater morphology resulting from the collapse of cylindrical shallow wells in glass beads was recently studied [20,21]. Unlike the collapse of shallow wells, subsidence cratering involves the collapse of underground pressurized gas cavities.…”

A new column collapse apparatus for the characterisation of the flowability of granular materials

“…Kinematic fields are extracted from image analysis by particle image velocimetry (PIV) [56], a widespread technique for the study of steady-state flows down inclines in both dry [37,57,58] and saturated [59,60] conditions. PIV analysis has been further incorporated to granular column collapse experiments [25,26,30,40,61] and similar set-ups [62]. We use the open-source software PIVlab [63], which implements a cross-correlation algorithm performing iterative deformation and refinement of all interrogation areas in each frame pair being processed.…”

“…where E tot is the total energy of the granular system, which is conserved, E pot = mgz CM is the gravitational potential energy, where z CM is the height of the centroid of the granular system, E kin = E trans kin + E rot kin is the kinetic energy, described by the mean square of the velocity fields resulting from the PIV analysis [62], and U is the internal energy of the granular system, which accounts for the energy dissipated during flow. We compute E kin by the addition of the translational E trans kin = mv 2 /2 and rotational E rot kin = Iω 2 /2 contributions, where I ≈ md 2 50 /10 is the moment of inertia of the granular system, approximated by the sum of the moments of inertia of all the particles assumed spherical, and ω = (∂v z /∂x, ∂v x /∂z) is the average angular velocity field in each time step.…”

“…Finally, in all cases, the increase of internal energy U at the final static state is equal to the reduction of E pot . According to [62], the continuous decay of E pot and the peak trend of E trans kin suggest that the initial collapse (first flow stage) is dominated by gravity whereas flow propagation (sec-ond and third flow stages) is governed by dissipation processes. Consistently, we attribute the increase of U mainly to irreversible particle interactions, including plastic normal collisions and the work of tangential forces and torques [73].…”