*Stiffness dependence of granular flow under gravity. *

**Abstract:**
The steady granular flow under gravity is investigated numerically in the hard-sphere limit
of the soft-sphere model with keeping the restitution coefficient constant. We find distinctively
different limiting behaviors for the two flow regimes, i.e., the collisional flow and
the frictional flow. In the collisional flow, the hard-sphere limit is straightforward;
the number of collisions per particle per unit time converges to a finite value and the total
contact time fraction with other particles goes to zero. For the frictional flow, however, we
demonstrate that the collision rate diverges as the power of the particle stiffness so that the
time fraction of the multiple contacts remains finite even in the hard-sphere limit, although
the contact time fraction for the binary collisions tends to zero. The results can be useful to
clarify the transition between the two flow regimes.