Angle of repose

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Angle of repose

The angle of repose (sometimes incorrectly confused with the 'angle of internal friction') is an engineering property of granular materials. It is the maximum angle of a stable slope determined by friction, cohesion and the shapes of the particles.

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. Material with a low angle of repose forms flatter piles than material with a high angle of repose. In other words, the angle of repose is the angle a pile forms with the ground.

Applications of theory

Talus cones on north shore of Isfjorden, Svalbard, Norway, showing angle of repose for coarse sediment.

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. It can also be used 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 determining the correct calculus of stability in vessels.

It is also commonly used by mountaineers as a factor in analyzing avalanche danger in alpine areas.

Measurement

There are numerous methods for measuring angle of repose and each produces slightly different results. Results are also sensitive to the exact methodology of the experimenter. As a result, data from different labs is not always comparable. One method is the triaxial shear test, another is the direct shear test.

Exploitation by antlion larvae

Sand pit trap of the antlion

The larva of the antlion traps small insects such as ants by digging a conical pit in loose sand, such that the slope of the walls is very close to the angle of repose for the sand.^[1] Thus, when a small insect blunders into the pit, its weight causes the sand to collapse below it, drawing the ant toward the center where the antlion larva lies in wait. The antlion larva assists this process by vigorously flicking sand out from the center of the pit when it detects a disturbance, undermining the pit walls and causing them to collapse toward the center, bringing the prey with them.

See also

The angle of repose plays a part in several topics of technology and science, including:

• Aberfan
• Avalanche
• Barchan
• Bulk cargo
• Eolian processes
• Fort Peck Dam
• Gaillard Cut
• Mass wasting
• Oceanic trench
• Sand volcano
• Scree
• Concrete slump test

References