  Model experiments are reported on the build-up of granular piles in two
dimensions. These show that as the initial density of falling grains is
increased, the resulting pile has decreasing final density and its coordination
number approaches the low value predicted for the theoretical marginal rigidity
state. This provides the first direct experimental evidence for this state of
granular matter. We trace the decrease in the coordination number to the
dynamics within an advancing yield front between the consolidated pile and the
falling grains. We show that the front's size increases with initial density,
diverging as the marginal rigidity state is approached.
