PHYSICS OF ANGLE OF REPOSE

 



The balance of forces on a stable slope

Stable slope and Angle of Repose

The angle of repose is the steepest angle that a stable slope can attain. In this situation, the force that pulls the particles down the slope (shear stress) is equal to and balanced by another force that resists the down-slope movement (shear strength).


Shear Stress on the Slope

Shear stress is the component of gravitational force that is parallel to the slope and causes particles to move down-slope. The component that is perpendicular to the slope surface is called the normal stress. It contributes to the friction between the particles and the surface. Shear stress increases with the angle of the slope, and when the surface is level there is no shear stress.

Shear stress on a slope
No shear stress on level ground
Greater shear stress on steeper slope


Shear Strength on the Slope

Shear strength is the resistance of particles to move down-slope. It acts against the shear stress and is determined by the inter-particle friction, and cohesion, which could be affected by the water content. If the particles on the slope have larger shear strength, then it could resist more shear stress on a steeper slope, resulting in a greater angle of repose.

Since rice has higher shear strength, it can resist a higher shear stress at a greater angle. This is why rice has a higher angle of repose than mung beans in my experiments.

Greater shear strength gives rice a greater angle of repose

Weaker shear strength gives mung beans a smaller angle of repose  



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