Study of the collapse of granular columns using two-dimensional discrete-grain simulation

Numerical simulations of the collapse and spreading of granular columns onto a horizontal plane using the Contact Dynamics method are presented. The results are in agreement with previous experimental work. The final shape of the deposit appears to depend only on the initial aspect ratio a of the column. The normalized runout distance has a power-law dependence on the aspect ratio a, a dependence incompatible with a simple friction model. The dynamics of the collapse is shown to be mostly controlled by a free fall of the column. Energy dissipation at the base of the column can be described simply by a coefficient of restitution. Hence the energy available for the sideways flow is proportional to the initial potential energy $E_0$. The dissipation process within the sideways flow is approximated well by basal friction, unlike the behaviour of the runout distance. The proportion of mass ejected sideways is shown to play a determining role in the spreading process: as a increases, the same fraction of initial potential energy $E_0$ drives an increasing proportion of the initial mass against friction. This gives a possible explanation for the power-law dependence of the runout distance on a. We propose a new scaling for the runout distance that matches the data well, is compatible with a friction model, and provides a qualitative explanation of the column collapse.