In article ,
"Toy" writes:
 "Marcus Fox" wrote in
 message ...

 I am trying to calculate a formula to determine approximately how much
 earth/material I would need to create a "pile"  ...

 The pile will be approximately cone shaped, and I know the formula to
 calculate the volume of a cone. 1/3 pi r2 (base radius) x height. ...
It's more general than that. The volume of anything that goes from
a point to a flat area by straight lines is 1/3 of the area multiplied
by the distance from the point to the plane of the flat area. The
same formula applies to cones, pyramids, ones that lean sideways, and
irregular shapes.
 However,
 since the soil will spread out and the base gets wider as the height
 increases, I need to know to what degree this will happen, for example
 what
 is the smallest slope in degrees where the pile will remain stable? 45? If
 this is the case then the radius of the base will be the same as the
 height.

 first it depends on the material.

 sand would have a shallower base angle for instance.

 if you have the same amount of material and it starts to spread out, without
 adding more material, the volume remains the same.

 or am I missing something here.
No, you are correct. To a first approximation, material poured onto
a pile will form a structure of the shape that the above formula
applies to  look at spoil heaps etc.
And the angle depends critically on the material and its dampness.
really dry sand may support only 15 degrees above the horizontal;
wet sand may reach 60. Earth is more cohesive than sand.
Regards,
Nick Maclaren.
