  We report experimental and numerical results on the growth of a super stable
heap (SSH). Such a regime appears for flows in a thin channel and for high flow
rate : the flow occurs atop a nearly static heap whose angle is stabilized by
the flowing layer at its top and the side wall friction. The growth of the
static heap is investigated in this paper. A theoretical analysis inspired by
the BRCE formalism predicts the evolution of the growth process, which is
confirmed by both experiments and numerical simulations. The model allows us to
link the characteristic time of the growth to the exchange rate between the
"moving" and "static" grains. We show that this rate is proportional to the
height of the flowing layer even for thick flows. The study of upstream
traveling waves sheds new light on the BCRE model.
