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A: Ray Cocco, Particulate Solid Research Inc., says:

The angle of slide is the angle at which a material begins to avalanche and the point at which the material can no longer hold itself up in a pile. This angle is the minimum slope measured in degrees before a loose solid material begins to flow due to gravity. The angle of repose is the steepest angle of solid material that can be piled. Basically, this angle is how material freely forms into a pile before avalanching. The angle of repose is similar to the angle of slide, and these measurements most often have similar values despite the different testing methods used to find these two values.

The internal angle of friction (or effective internal angle of friction) is the measure of the maximum amount of shear stress a bulk solid material can sustain. This material behavior is responsible for the ratholing phenomena we see in hoppers. Essentially, a rathole forms when the material is strong enough to maintain a funnel shape despite the force of the material on top of it. Particle shape, roughness, elasticity, moisture levels, size, size distribution, and other material attributes all play a role in the material strength.

The main difference between a material’s internal angle of friction and its angle of repose is the weight of the material on top of it. The internal angle of friction is a measurement that takes into consideration the normal force of the material on top. In other words, the weight of the material above and how that material interlocks under such load is quantified with an internal angle of friction. The angle of repose is based on a material’s behavior when no material is on top of the material pile at the point of avalanche or strength failure.

Measurements are typically obtained with a shear test unit where the point of material strength failure is recorded for several normal forces on that material. The angle of repose (or slide) has no normal force on top of the material other than gravity.

With hopper flow, most of the material sees a significant amount of force on top. This is why a good hopper design uses the internal angle of friction. Using the angle of repose to design a hopper could result in funnel-flow behavior where mass-flow behavior is desired. Funnel-flow behavior comes with a whole host of hopper issues, including erratic inventory aging, feeding issues, and even structural issues with the hopper.


Ray Cocco is the president and CEO at Particulate Solid Research Inc.