## Paste-Void Proximity

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.

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