Continuous to intermittent flows in growing granular heaps

If a granular material is poured from above on a horizontal surface between two parallel, vertical plates, a sand heap grows in time. For small piles, the grains flow smoothly downhill, but after a critical pile size ${X}_{c}$, the flow becomes intermittent: sudden avalanches slide downhill from the apex to the base, followed by an ``uphill front'' that slowly climbs up, until a new downhill avalanche interrupts the process. By means of experiments, controlling the distance between the apex of the sandpile and the container feeding it from above, we show that ${X}_{c}$ grows linearly with the input flux, but scales as the square root of the feeding height. We explain these facts from a phenomenological model based on the experimental observation that the flowing granular phase forms a ``wedge'' on top of the static one, differently from the case of stationary heaps. Moreover, we demonstrate that our controlled experiments allow to predict the value of ${X}_{c}$ for the common situation in which the feeding height decreases as the pile increases in size.