Granular collapse in two dimensions

Abstract

An experimental investigation is conducted into the collapse of granular columns inside rectangular channels. The final shape is documented for slumps inside relatively wide channels, and for collapses inside much narrower slots. In both cases, the collapse is initiated by withdrawing a swinging gate or sliding door, and the flow remains fairly two-dimensional. Four different granular media are used; the properties of the materials vary significantly, notably in their angles of friction for basal sliding and internal deformation. If H is the initial height of the column, h ∞ the maximum final height of the column and a the initial aspect ratio, then the data suggest that H/ h ∞ ∼ a 0.6 in wide channels and H/ h ∞ ∼ a 0.5 for narrow slots. For the runout, we find that (l ∞ − L)/L ∼ a 0.9±0.1 for wide channels, and (l ∞ − L)/L ∼ a 0.65±0.05 or l ∞ /L ∼ a 0.55±0.05 for narrow slots, where l ∞ is the maximum runout of the material and L the initial length of the column along the channel (a := H/L). In all cases, the numerical constant of proportionality in these scaling relations shows clear material dependence. In wide slots, there is no obvious universal scaling behaviour of the final profile, but such a behaviour is evident in narrow slots. The experimental results are compared with theoretical results based on a shallow granular-flow model. The qualitative behaviour of the slump in the wide slot is reproduced by the theoretical model. However, there is qualitative disagreement between theory and the experiments in the narrow slot because of the occurrence of secondary surface avalanching.

Sensitivity to solid volume fraction of gravitational instability in a granular medium

“…To highlight the dynamics of the destabilization process, we have used a dambreak like protocol almost analogous to previous works [16][17][18][19][20] which allows us to initiate a gravitational instability at any inclination, independently of the solid volume fraction of sample. The questions to be addressed here are the following:…”

“…This dam-break configuration is achieved experimentally either by rapidly raising the retaining walls [16][17][18][19], or by removal of a confinement force [20]. Experiments [16][17][18][19][20] and numerical simulations [21,22] have been carried out on several granular pile geometries and scaling laws have been proposed to relate the dimensions of the residual deposit to the initial aspect ratio of the pile. What is the role of the initial structure of the granular packing?…”

Granular collapse in a fluid: Role of the initial volume fraction

“…The same problem has been also investigated in a two dimensional geometry, the so-called dam-break problem. [8][9][10][11][12][13] In this case the granular material is initially confined by a wall, which is suddenly removed. The observed scaling characterizing the deposit morphology is different from the axisymmetric case but the aspect ratio remains the relevant parameter, as long as the channel is wide enough to prevent additional frictional effects on the side walls.…”

“…The observed scaling characterizing the deposit morphology is different from the axisymmetric case but the aspect ratio remains the relevant parameter, as long as the channel is wide enough to prevent additional frictional effects on the side walls. 9 The granular collapse has been also studied using numerical simulations based on discrete element methods, allowing a precise study of the internal structure of the flow. [13][14][15][16] From a theoretical point of view, the spreading has been described using depth averaged equations.…”

Slumps of viscoplastic fluids on slopes

“…In fact the various dam-break solutions provide important test cases for numerical solvers, which are then applied to more complicated problems. Important studies of this type of motion have included: inertially dominated flows [8][9][10], viscously dominated flows [11,12], the collapse of granular columns [13][14][15] and the flow of viscoplastic fluids [7,16,17].…”