Exploring the relationship between critical state friction angle and angle of repose using the discrete element method

In granular materials, the critical state friction angle (ϕ_cs) and the angle of repose (AOR) are widely used to characterize shear strength and slope stability. Despite their frequent use, the equivalence between these two angles remains unclear, particularly in light of differing procedures used to determine AOR. This study examines whether ϕ_cs and AOR are intrinsically related and identifies the conditions under which they may coincide. A calibrated 2D Discrete Element Method (DEM) model was employed to systematically investigate the influence of particle shape on both ϕ_cs and AOR. Four particle shapes, ranging from circular discs to angular polygons, were used, with angularity controlled through the corner number. Additionally, four commonly adopted repose methods were used. The results show that particle shape exerts a strong influence on macro- micro-mechanical behavior, with both ϕ_cs and AOR increasing monotonically with particle angularity. However, the correspondence between ϕ_cs and AOR is found to be repose method dependent. Reposing employing side-wall confinement, impact particle rearrangement, and suppressing the development of fabric anisotropy, leading to higher coordination numbers and AOR values that significantly exceed ϕ_cs. In contrast, repose methods allowing free deposition on flat frictional surfaces promote the development of force anisotropy consistent with the critical-state fabric in shearing, resulting in AOR values that closely match ϕ_cs across all particle shapes. These findings demonstrate that AOR and ϕ_cs are linked through the evolution of contact force anisotropy and that, with appropriate repose method selection, AOR can serve as a reliable and practical proxy for ϕ_cs.