Granular collapse in two dimensions

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, $h_{\infty}$ the maximum final height of the column and $a$ the initial aspect ratio, then the data suggest that $H/h_{\infty} \,{\sim} a^{0.6}$ in wide channels and $H/h_{\infty} \,{\sim}\, a^{0.5}$ for narrow slots. For the runout, we find that $(l_{\infty}\,{-}\,L)/L \,{\sim}\, a^{0.9\pm 0.1}$ for wide channels, and $(l_{\infty}\,{-}\,L)/L \,{\sim}\, a^{0.65\pm0.05}$ or $l_\infty/L \,{\sim}\, a^{0.55\pm0.05}$ for narrow slots, where $l_{\infty}$ 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.