Granular slumping on a horizontal surface

We report the results of an experimental investigation of the flow induced by the collapse of a column of granular material (glass beads of diameter $d$⁠) over a horizontal surface. Two different setups are used, namely, a rectangular channel and a semicircular tube, allowing us to compare two-dimensional and axisymmetric flows, with particular focus on the internal flow structure. In both geometries the flow dynamics and the deposit morphologies are observed to depend primarily on the initial aspect ratio of the granular column $a=Hi∕Li$⁠, where $Hi$ is the height of the initial granular column and $Li$ its length along the flow direction. Two distinct regimes are observed depending on $a$⁠: an avalanche of the column flanks producing truncated deposits for small $a$ and a column free fall leading to conical deposits for large $a$⁠. In both geometries the characteristic time scale is the free fall of the granular column $τc=Hi∕g$⁠. The flow initiated by Coulomb-like failure never involves the whole granular heap but remains localized in a surface layer whose size and shape depend on $a$ and vary in both space and time. Except in the vicinity of the pile foot where the flow is pluglike, velocity profiles measured at the side wall are identical to those commonly observed in steady granular surface flows: the velocity varies linearly with depth in the flowing layer and decreases exponentially with depth in the static layer. Moreover, the shear rate is constant, $γ̇=0.3g∕d$⁠, independent of the initial aspect ratio, the flow geometry, position along the heap, or time. Despite the rather complex flow dynamics, the scaled deposit height $Hf∕Li$ and runout distance $ΔL∕Li$ both exhibit simple power laws whose exponents depend on $a$ and on the flow geometry. We show that the physical origin of these power laws can be understood on the basis of a dynamic balance between acceleration, pressure gradient, and friction forces at the foot of the granular pile. Two asymptotic behaviors can be distinguished: the flow is dominated by friction forces at small $a$ and by pressure forces at large $a$⁠. The effect of the flow geometry is determined primarily by mass conservation and becomes important only for large $a$⁠.