Static and flowing regions in granular collapses down channels

Through laboratory experiments we investigate inertial granular flows created by the instantaneous release of particulate columns into wide, rectangular channels. These flows are characterized by their unsteady motion, large changes of the free surface with time, and the propagation towards the free surface of an internal interface separating static and flowing regions. We present data for the time-dependent geometry of the internal interface and the upper, free surface for aspect ratios, a , in the range from 3 to 9.5 (where a = h i ∕ d i is the ratio of the initial height to basal width of the column). The data were analyzed by two different approaches. First, by integrating under the entire internal interface we obtained data for the static area, A D , as a function of time for different a . Second, in order to characterize vertical deposition rates, we measured the thicknesses of the flowing region, h F ( x , t ) , and the static region, h D ( x , t ) , at fixed horizontal positions, x , and time, t , since the initiation of the experiment. We also determined detailed velocity profiles with depth at distances scaled to the final maximum runout distance to analyze the kinematic behavior of the flowing layer. In the initial free-fall phase, the temporal variation of the static area is independent of h i and scales as g d i t . During the subsequent lateral spreading phase, A D ( t ) varies linearly with time and the nondimensional deposition rate ( d A D ∕ d t ) ∕ ( g d i 3 ) 1 ∕ 2 is a linear function of a . The thickness of the interface h D ( x , t ) at constant x depends on a and varies linearly with time. The local deposition rate ∂ h D ∕ ∂ t is not constant along the flow length. Data show that for the major part of the flow length ∂ 2 h D ∕ ∂ t ∂ x is constant. In the lateral spreading phase, the velocity profiles are characteristically linear with a basal exponential region, a few grains in thickness, which separates static from moving regions. The shear rate is a constant dependent on a modified initial height h ̃ i as ( g ∕ h ̃ i ) 1 ∕ 2 , where h ̃ i is a characteristic length scale in the system describing the fraction of the granular column actually involved in the flowing region.