Steepest angle at which granular materials can be piled before slumping
For the Wallace Stegner novel, see Angle of Repose. For the angle of friction between two solid objects, see Friction § Angle of friction.
Angle of repose of a heap of sandSandpile from the Matemateca (IME-USP) collection
The angle of repose, or critical angle of repose,[1] of a granular material is the steepest angle of descent or dip relative to the horizontal plane on which the material can be piled without slumping. At this angle, the material on the slope face is on the verge of sliding. The angle of repose can range from 0° to 90°. The morphology of the material affects the angle of repose; smooth, rounded sand grains cannot be piled as steeply as can rough, interlocking sands. The angle of repose can also be affected by additions of solvents. If a small amount of water is able to bridge the gaps between particles, electrostatic attraction of the water to mineral surfaces increases the angle of repose, and related quantities such as the soil strength.
When bulk granular materials are poured onto a horizontal surface, a conical pile forms. The internal angle between the surface of the pile and the horizontal surface is known as the angle of repose and is related to the density, surface area and shapes of the particles, and the coefficient of friction of the material. Material with a low angle of repose forms flatter piles than material with a high angle of repose.
The term has a related usage in mechanics, where it refers to the maximum angle at which an object can rest on an inclined plane without sliding down. This angle is equal to the arctangent of the coefficient of static friction μs between the surfaces.
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Mehta, A.; Barker, G. C. (1994). "The dynamics of sand". Reports on Progress in Physics. 57 (4): 383. Bibcode:1994RPPh...57..383M. doi:10.1088/0034-4885/57/4/002. S2CID 250898376.
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