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# Results and Discussion

Figure 1 illustrates 2-D slices from the 3-D concrete microstructural model for the coarse and fine limits of the fine aggregate particle size distribution. In these images, one can clearly see that the system containing smaller aggregates contains much more paste (blue) within 100 µm of a LWFA surface. In fact, the surface area of the LWFA in the righthand portion of Fig. 1 is about double that of its surface area in the lefthand half of the figure, as is the volume of paste within 100 µm of the LWFA.

Figure 1: Model 2-D images (20 mm x 30 mm, 1 pixel= 100 µm) from 3-D continuum concrete microstructures with 50% replacement of fine aggregate by LWFA. Colors are as follows: white- cement paste farther than 100 µm from a LWFA surface, blue- cement paste within 100 µm of a LWFA surface, red- normal weight aggregates, and yellow- saturated LWFAs. In the left image, Vagg=0.75 and fine aggregate follows coarse limit of ASTM C 33 specification. In the right image, Vagg=0.70 and fine aggregate follows fine limit of ASTM C 33 specification.

The two microstructures are evaluated quantitatively in Figure 2 which shows, for the two aggregate PSDs and volume fractions, the fraction of the cement paste within a given distance of a LWFA surface. Clearly, to disperse the water uniformly throughout the microstructure at a low level of fine aggregate replacement, the surface area of the fine aggregate (or specifically the saturated LWFA) should be maximized. Thus, equation (2) provides only a detemination of the bulk volume of water needed for curing, while the detailed simulation or equations of Lu and Torquato [6] are needed to ensure that the majority of the cement paste is near enough to a LWFA surface to benefit from the available water.

Figure 2: Model results for fraction of cement paste within a given distance of the LWFA surfaces for three replacement levels and two aggregate gradations: top- Vagg=0.75 with coarse limit for fine aggregate, and bottom- Vagg=0.70 with fine limit for fine aggregate. Symbols indicate simulation data and lines correspond to the estimations of the equations developed by Lu and Torquato [5] (modified by considering only the paste and LWFA components of the system).

This result is in agreement with the protected paste volume concept for air voids, which suggests that a finely dispersed system of small air voids will be superior to one composed of larger air voids, at equal air contents. In fact, once the water in the LWFA is consumed by hydration, a system of relatively coarse air voids should be left behind to aid in freeze/thaw protection. Past studies have indeed indicated a high durability for lightweight aggregate concrete exposed to freezing and thawing cycles [17].

For the three replacement levels and two aggregate gradations considered in this study, the approximations based upon the analytical equations of Lu and Torquato [6] are seen to estimate quite well the simulation results, especially at short distances and for complete replacement of the fine aggregates by their lightweight counterparts. The evaluation of these equations requires much less computer time than the full 3-D microstructural model simulation and conveniently provides the fraction of cement paste within all distances of interest to the user.

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