The angle of repose or the critical angle of repose,〔
〕 of a granular material is the steepest angle of descent or dip relative to the horizontal plane to which a 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°. Smooth, rounded sand grains cannot be piled as steeply as can rough, interlocking sands. If a small amount of water is able to bridge the gaps between particles, electrostatic attraction of the water to mineral surfaces will increase soil strength.
When bulk granular materials are poured onto a horizontal surface, a conical pile will form. 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. However, a 2011 study shows that the angle of repose is also gravity-dependent.〔
〕 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 ''μ''s between the surfaces.
== Applications of theory ==
The angle of repose is sometimes used in the design of equipment for the processing of particulate solids. For example, it may be used to design an appropriate hopper or silo to store the material, or to size a conveyor belt for transporting the material. It can also be used in determining whether or not a slope (of a stockpile, or uncompacted gravel bank, for example) will likely collapse; the talus slope is derived from angle of repose and represents the steepest slope a pile of granular material will take. This angle of repose is also crucial in correctly calculating stability in vessels.
It is also commonly used by mountaineers as a factor in analysing avalanche danger in mountainous areas.
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