The repose of granular materials is investigated via two different Discrete Element Method (DEM) implementations in comparison with an experimental reference from a recently proposed benchmark setup. On a methodological standpoint, a rigorous measurement method of the angle of repose (AOR) is first proposed for plane-strain and axisymmetric conditions as encountered in the reference experiments. Additionally, two systematic procedures are designed in order to also determine the void ratio of the heap, as a fundamental property of granular matter possibly influencing the AOR. A physical discussion is then developed on the role of particle shape, considering the nonspherical nature of reference particles with a convexity value of C = 0.954. Adoping non-convex multi-spheres aggregates (i.e. clumps), the first DEM modelling approach successfully predicts the AOR within a 8% tolerance. After a convex simplification that neglects local concavities, another approach based on potential particles underestimates to a greater extent the AOR, bringing it down from 35.95 ± 0.88 • to 31.26 ± 0.95 •. For the loading setup(s) at hand, the AOR is eventually shown to bear no constitutive nature. It is for instance independent of initial void ratio but is still different than the critical friction angle. The latter may actually serve as a lower bound for the process-dependent AOR. These conclusions are drawn from a statistical analysis of a large set of results, accounting for the random nature of the microscopic arrangement in the studied process.