Next: Spacing Distributions
The efficacy of entrained air voids in concrete for providing freeze-thaw durability has been known since the 1940's. However, their exact role in freeze-thaw durability has not been established definitively. There appears to be a connection between the expansion of the water during freezing and the proximity of the air voids.
Regardless of which particular physical theory of freeze-thaw degradation might be correct, an undisputed fact is that good freeze-thaw durability can be achieved through the presence of many small entrained air voids distributed throughout the cement paste phase of the concrete. Therefore, one could characterize an air void system by estimating some measure of air void "spacing," with the expectation that concretes with equal air contents, but different air void spacings, should exhibit different freeze-thaw performance.
One of the first attempts to characterize the "spacing" of air voids was by Powers, which was the basis for the American Society for Testing and Materials (ASTM) C 457 spacing factor (). Since then, spacing equations have been proposed by Philleo, Attiogbe, and Pleau and Pigeon. Each of these equations attempts to characterize the "spacing" of voids in air-entrained concrete, even though the Attiogbe equation estimates the spacing among air voids, and the other equations estimate the distance water must travel to reach the nearest air void.
At present, evaluation of an air void spacing equation consists of a comparison between the estimate of spacing and the results of laboratory freeze-thaw experiments[7,8]. The a priori assumption is that each equation is inherently correct in its estimate of spacing. Unfortunately, each of these spacing equations proposed for predicting freeze-thaw performance has inherent assumptions or simplifications built into its development. Until now, no quantitative measure has been made of the effects due to these assumptions.
This paper quantifies the performance of the various spacing equations using a computerized numerical experiment. The computer experiment measures various "spacing" quantities in a paste-air system. Systems are composed of air voids with either monosized or lognormally distributed radii. Since the size and the location of each sphere are known exactly, the actual "spacings" can also be calculated exactly. To achieve acceptable statistics, the results from many system realizations are used to estimate averaged quantities. These results, along with the associated spacing equation predictions, are reported for comparison.