Angle of repose (${\theta }_r$)

The angle of repose characterizes the free-surface slope of a resting granular material, measured relative to horizontal under a specified preparation protocol. A slowly poured dry sand pile often forms an approximately conical surface, with slope $\tan {\theta }_r$. It is a bulk consequence of contact friction, particle shape, packing and any cohesion, rather than a universal constant of one chemical substance.

A simple comparison is to pour a pile through a funnel, measure its height and base radius, and infer the slope from their ratio. A second experiment slowly tilts a layer until it avalanches. The onset angle and the angle after flow stops can differ, so reports should state which quantity was measured. For a single sliding block, static balance suggests $\tan \theta =\mu$, but identifying a pile's angle of repose with a microscopic coefficient of friction ignores rearrangement and collective contact geometry.