# Measurement of Piles of Soil

## This Sounds a Lot Like Math…

And that’s because it is. Come on! I got into construction so I didn’t have to deal with math, right? Wrong. It’s ok, we’ll give you some easy solutions, because at the end of the day, you could make your company some money (or yourself), impress your boss and make a good name for yourself.

## Angle of Repose

Can we all agree that if you were to dump a pile of sand, one possible shape is the cone? What else might a pile of dirt look like? A pyramid? A wedge? A rectangular pyramid? Sure. The angle of repose is the angle above horizontal grade that the dirt rises in this pile. This is a fancy way of saying the slope of the soil. Imagine what a pile of wet sand might look like compared to a pile of dry sand, or moist earth. You could imagine the moist earth might reach taller and steeper than the dry sand.

 Angle of Repose Smooth Gravel 30 Sharp Gravel 40 Dry Sand 25 to 35 Moist Sand 30 to 45 Wet Sand 20 to 40 Cement 37

How did they come up with these angles? I don’t know and I don’t want to know, so I can’t tell you. Sorry. Wikipedia can probably tell us. We just want to use this information and move on with life.

## What You Came For – Formulas

Ok, so what everyone wants to know (what the lazy side of me always wants to know) is the formula. Just tell me the formula so I can plug and chug and get a good number and move on with life. Prepare yourself for a blast from the past – we’re headed towards geometry – I think.

V=3hr2

V=6hb(2a+a1)

V=61hb3a2htan

## Formula for Frustum (Volume Between 2 Parallel Planes) of a Rectangular Pyramid:

V=6h(ab+(a+a1)(b+b1)+a1b1)

## I Need More

That’s right, you need to know some more information in order to solve for the equations above. We have some variables that should be identified with the help of a drawing. Then we’ll look at some examples to see how easy (or not) it is to solve for these equations.

h= height of the object
r= radius of the cone-shaped dirt pile
a= length of the wedge or frustum of a rectangular pyramid
a1= upper length of wedge or frustum
b= width of the wedge or frustum of a rectangular pyramid
b1= upper width of wedge or frustum
=  angle of repose, lengthwise
2= angle of repose, widthwise