Next: Philleo Spacing Equation
Up: Spacing Equations
Previous: Spacing Equations
The most widely used paste-void spacing equation is the Powers spacing factor[2]. Contrary to a popular misconception, it does not attempt to estimate the distance between air voids. Rather, it is an attempt to calculate the fraction of paste within some distance of an air void (paste-void proximity). The Powers equation approximates the distance from the surface of all the air void surfaces which would encompass some large fraction of the paste. However, the value of this fraction is not quantified.
The second misconception is that the Powers spacing factor represents the maximum distance water must travel to reach the nearest air void in a concrete specimen[3,8,17]. From the previous discussion of the distribution of paste-void and void-void spacings, it should be clear that there is no single theoretical maximum value for the paste-void spacings. One can only quantify percentiles of the distribution to characterize the fraction of paste within some distance to the nearest air void surface. In practice, the maximum paste-void spacing is the size of the sample.
The Powers spacing factor was developed using two idealized systems. For small values of the p/A ratio, there is very little paste for each air void. Powers used the ``frosting'' approach of spreading all of the paste in a uniformly thick layer over each air void. The thickness of this ``frosting'' is approximately equal to the ratio of the volume of paste to the total surface area of air voids,
For large values of the p/A ratio, Powers used the cubic lattice approach. The spheres are placed at the vertices of a simple cubic array. The air voids are monosized, each with a specific surface area equal to the bulk value. The cubic lattice spacing is chosen such that the air content equals the bulk value. The resulting Powers spacing factor is the distance from the center of a unit cell to the nearest air void surface,
The p/A value of 4.342 is the point at which these two equations are equal.
The intent was that a large fraction of the paste should be within
of an air void surface. An acceptable value of 
for
good freeze-thaw performance was determined from estimating material
properties of concrete.