  Granular column collapse is a simple but important problem to the granular
material community, due to its links to dynamics of natural hazards, such as
landslides and pyroclastic flows, and many industrial situations, as well as
its potential of analyzing transient and non-local rheology of granular flows.
This article proposes a new dimensionless number to describe the run-out
behaviour of granular columns on inclined planes based on both previous
experimental data and dimensional analysis. With the assistance of the
sphero-polyhedral discrete element method (DEM), we simulate inclined granular
column collapses with different initial aspect ratios, inter-particle
frictions, and initial solid fractions on inclined planes with different
inclination angles (2.5$^{\circ}$ - 20.0$^{\circ}$) to verify the proposed
dimensional analysis. Detailed analyses are further provided for better
understanding of the influence of different initial conditions and boundary
conditions, and to help unify the description of the relative run-out distances
of systems with different inclination angles. This work determines the
similarity and unity between granular column collapses on inclined planes and
those on horizontal planes, and helps investigate the transient rheological
behaviour of granular flows, which has direct relevance to various natural and
engineering systems.
