  Gravity-driven turbulent bedload transport has been extensively studied over
the past century in regard to its importance for Earth surface processes such
as natural riverbed morphological evolution. In the present contribution, the
influence of the longitudinal channel inclination angle on gravity-driven
turbulent bedload transport is studied in an idealised framework considering
steady and uniform flow conditions. From an analytical analysis based on the
two-phase continuous equations, it is shown that : (i) the classical slope
correction of the critical Shields number is based on an erroneous formulation
of the buoyancy force, (ii) the influence of the slope is not restricted to the
critical Shields number but affects the whole transport formula and (iii)
pressure-driven and gravity-driven turbulent bedload transport are not
equivalent from the slope influence standpoint. Analysing further the granular
flow driving mechanisms, the longitudinal slope is shown to not only influence
the fluid bed shear stress and the resistance of the granular bed, but also to
affect the fluid flow inside the granular bed - responsible for the transition
from bedload transport to debris flow. The relative influence of these coupled
mechanisms allows us to understand the evolution of the vertical structure of
the granular flow and to predict the transport rate scaling law as a function
of a rescaled Shields number. The theoretical analysis is validated with
coupled fluid-discrete element simulations of idealised gravity-driven
turbulent bedload transport, performed over a wide range of Shields number
values, density ratios and channel inclination angles. In particular, all the
data are shown to collapse onto a master curve when considering the sediment
transport rate as a function of the proposed rescaled Shields number.
