Question #270503 on Yade changed:
https://answers.launchpad.net/yade/+question/270503

    Status: Open => Answered

Bruno Chareyre proposed the following answer:
Hello,
It can't be "right" or "wrong" in the sense you think to it.
It is just a normalization equation such that scaling all particle sizes by the 
same factor will keep macroscale cohesion exactly the same.

If you multiply by a constant (pi, sqrt(2), or any other magic number)
it is yet another valid normalization. But why would you do that?
Multiplying by 1 is the simplest thing.

I don't think there is a mention of contact area in the documentation (is 
there?). Taking contact area as the projected area of the smallest sphere would 
be an assumption (here we don't do any assumption, we just normalize).
You know how the equations are, so if you really want to introduce this 
assumption you can simply multiply the material cohesion by pi (note that 
material cohesion is a macroscale variable, not something supposed to reflect 
some cement property at the microscale, so there is no inconsistency in 
multiplying it by pi).
HTH
Bruno

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