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Q & A: Sand Piles

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Most recent answer: 04/18/2015
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 olí 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. 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." There's a nice article on it on Wikipedia: . 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.

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.

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 (mods by mw)

(published on 10/22/2007)

Follow-Up #1: pressure in sandpiles

Hello, If the sand comes mixed in with a fluid and deposits against a wall say, which forces a 90 degree angle of repose, what pressure distribution would you say it develops? What would you keep in mind when thinking about this?If I remember my sand castles correctly, they needed a bit of compaction to stay vertical (small or zero pressure against the way, i.e. if there was a wall, I could remove it without the pile falling down). Who is studying this issue? Thanks a lot!
- Juan Tello (age 35)

This is a tough topic. Rather than try to give our own shaky answers (some of which were wrong in the first version of the answer above) we'll steer you to those people you asked about who have worked on it.  Some of the best studies on it have been done by our friends Sue Coppersmith, Sid Nagel, and Heinrich Jaeger.

Here's a basic review on the topic: 

Here's a good public-domain paper on that pressure distribution issue: 

Mike W.

(published on 04/18/2015)

Follow-up on this answer.