ABSTRACT
Due to the fundamental interest as well as the numerous industrial applications (Jaeger et al. 1996), a great deal of both experimental (Drake 1991; Rajchenbach 2003; Johnson et al. 1990) and theoretical (Louge 2003) work has been devoted to the rheology of dry granular flows confined in a channel, but full understanding is still lacking. Numerous studies both experimental (Pouliquen 1996; Azanza et al. 1999) and numerical (Silbert et al. 2001; Prochnow 2002) displayed a wide variety of behaviours, sometimes incompatible with one another (Ancey 2002). When a granular material is poured on a bumpy inclined surface confined between sidewalls, two limiting flow regimes are observed. At low flow rates, the material is mobilized all the way to the base (Pouliquen 1996; Silbert et al. 2001).Above a minimum flow rate, a heap resembling a wedge forms at an inclination exceeding the angle of repose of a static pile. This “Super Stable Heap” (SSH) is made possible by a relatively thin rectilinear layer of constant thickness riding on its surface and confined between the two frictional walls (Fig. 1a). It was shown in the literature (Taberlet et al. 2003) that a SSH is dynamically stabilized by the flow at its surface and that solely side-wall friction is responsible for its formation. Using a balance of momentum for a mobilized layer, one can derive (Taberlet et al. 2003) an approximate linear scaling law linking the free surface angle, ϕ, the height of the layer, h, and the width of the channel, W :
ϕ
Q
Q
a) b)
ϕ
y
x
z
where µi and µw are effective friction coefficients (Taberlet et al. 2003). Thus, confining walls play a major role in the momentum balance if the second term on the right side of this equation dominates the first.
