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Paste-void proximity equations estimate the volume fraction of paste
within some distance
from the surface of the nearest air void.
There are two simple ways to visualize
this spacing: (1) Imagine surrounding each air void with a shell of
thickness *s*. These shells may overlap one another, but may not
overlap or penetrate air voids. The volume fraction of the paste that is
within any
shell is equivalent to the volume fraction of paste within a distance
*s* of an air
void surface.
(2) Given an air void system, pick points at random throughout
the paste which lie outside the air voids.
For each point, find the distance to the nearest air void
surface. The number fraction of the points that fall within a distance
*s* of an air void surface is equal to the
volume fraction of paste within a distance *s*
of an air void surface. This second approach is the one used here
to estimate the CDF of the spacing distribution.

This definition of the paste-void proximity distribution is the same as that used by proponents of the protected paste volume (PPV) concept [11,12,13]. The material parameters of the concrete determine the limiting spacing, and one wants to determine the fraction of paste within this distance to the nearest air void.