  This work generalises the granular integration through transients formalism
introduced by Kranz et al. [Phys. Rev. Lett. 121, 148002 (2018)] to the
determination of the pressure. We focus on the Bagnold regime, and provide
theoretical support to the empirical $\mu(\mathcal{I})$ rheology laws, that
have been successfully applied in many granular flow problems. In particular,
we confirm that the interparticle friction is irrelevant in the regime where
the $\mu(\mathcal{I})$ laws apply.
