  The law of $\mu(\mathcal{I})$ rheology has proven very successful to describe
the rheology of granular liquids. It however lacks theoretical support. From
the granular integration through transient formalism, we extract a simplified
model that expresses the rheology of granular liquids as a competition between
three time scales. In particular, this model allows to derive the
$\mu(\mathcal{I})$ law within a well defined theoretical framework. Outside of
the Bagnold flow regime, this framework predicts a non-trivial behavior of the
effective friction coefficient. Furthermore, the extension of the model to the
case of granular particles suspended in a viscous liquid provides an
explanation of the similarities observed experimentally between the evolution
of the friction coefficient in the suspension and the $\mu(\mathcal{I})$ law of
dry granular liquids.
