  The steady shear rheology of granular materials is investigated in slow
quasi-static states and inertial flows. The effect of the gravity field and
contact stiffness, which are conventionally trivialized is the focus of this
study. Series of Discrete Element Method simulations are performed on a weakly
frictional granular assembly in a split-bottom geometry considering various
gravity fields and contact stiffnesses. While traditionally the inertial
number, i.e., the ratio of stress to strain-rate timescales describes the flow
rheology, we find that a second dimensionless number, the ratio of softness and
stress timescales, must also be included to characterize the bulk flow
behavior. For slow, quasi-static flows, the density increases while the
macroscopic friction decreases with respective increase in particle softness
and gravity. This trend is added to the $\mu(I)$ rheology and can be traced
back to the anisotropy in the contact network, displaying a linear correlation
between macroscopic friction and deviatoric fabric in the steady state.
Interestingly, the linear relation holds when the external rotation rate is
increased for a given gravity field and contact stiffness.
