Q & A: Sand Piles

If sand is poured onto the floor in a small stream, it forms a pile that has some angle with respect to the ground. There is some maximum angle of the pile that cannot be exceeded, so my questions are what factors (e.g. speed of the stream, identity of the substance being poured) does this angle depend on, and how would you go about calculating it?
- Cynthia (age 17)
UIUC, good ol’ Champaign-Urbana, the middle of the corn

Cynthia -

When sand is poured into a pile, like you said, there is a specific angle which cannot be exceeded. What's more interesting than that, though, is that no matter how many times you pour the sand or how much sand you pour, the maximum angle won't change.

The maximum angle that the sand can make with the ground is called the "angle of repose." One thing that makes a big difference in the angle of repose is how wet the sand (or other material) is. That's why when you build a sand castle at the beach, it works best if you use wet sand. There's currently a lot of research going on trying to understand the physics of what happens to the physical properties of a granular material when you add water.

Another thing is that the larger the objects are, the steeper the angle of repose will be. For example, piled gravel will have a much steeper angle of repose than piled sand. Also, the amount of friction provided by the surface underneath the sand pile makes a difference. Sand piled on a sheet of sandpaper will move differently than sand piled on a sheet of ice.

So far it seems like it would be pretty straight-forward to calculate the angle of repose for something. Unfortunately, one of the things that influences the angle of repose is the shape of the object. If the grains of sand were perfectly round, they would slide against each other easily and the angle of repose would be pretty small. But sand isn't always perfectly round. It tends to be extremely irregular, and sand from different places will have different shapes. It's difficult to model how these shapes will interact when piled freely on top of each other. (For example, you can imagine if you piled a whole bunch of tetris pieces up - it would be pretty hard to determine how they would settle if you just dumped them in a pile.)

There are probably other things that influence the angle of repose - these are just some of the more important ones. There's plenty of physicists out there making their livings by studying just this sort of thing.

-Tamara

(published on 10/22/2007)