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Experimental Design

Because of the large number of variables that could potentially influence the chloride diffusivity of a concrete, a fractional factorial experimental design was selected to identify the subset of "significant" variables [5]. The seven variables examined and their low and high settings are given in Table 1. A 2^7-3 fractional factorial experimental design was selected to examine the effects of the seven listed variables in 16 runs. Standard design generators were used to determine the high and low settings for each of the sixteen runs to assure an orthogonal and a balanced design. In this way, the main variable effects can be determined free and clear from all interactions. Using this design, second-order interactions can also be estimated, but will be confounded (indistinguishable) amongst each other, since the number of computer runs is less than the number of possibilities of two variable combinations.

In addition to these 16 runs, one "center point" experiment was conducted with all of the seven variable settings at their mid-range values. For the coarse and fine particle size distributions, this mid-range was selected as the halfway point between the limits specified in the ASTM C33 standard [13] and shown in Figure 1. For two of the experiments with the higher volume fraction of aggregate and containing air voids, the air void content had to be reduced slightly from 10% to 8.5-9% to enable placement of all of the aggregate and air void particles, which together accounted for about 84% of the overall concrete volume, a rather dense packing even for a size distribution of spherical particles.

Once the most significant variables had been determined, a response surface design was developed to provide more quantitative information on their effects on the chloride diffusivity of concrete. From the initial 17 runs, w/c ratio, degree of hydration, and volume fraction of aggregates were determined to be significant. Six additional runs were then executed by varying each of these three variables between two extreme values while holding the other two at their mid-range value. The two extreme values were selected to be twice the distance from the mid-range value as the high and low settings shown in Table 1 (e.g., 0.4 and 0.8 for degree of hydration and 0.525 and 0.825 for volume fraction of aggregate). This choice of extreme values yields a response surface whose predicted values are estimated with equal precision at any fixed distance from the center point. However, for w/c ratio, this proved computationally impossible, so that values of 0.25 (instead of 0.15) and 0.75 were used as the two extremes. The other four variables were fixed at computationally convenient values for the additional response surface runs since they had been shown to have only negligible effects on the concrete diffusivity.

The response surface design allows estimation of a second-order equation. Because the chloride diffusivity of concrete varies over several orders of magnitude for the conditions examined in this study, the log of the diffusivity was used and the following equation was fitted by ordinary least squares regression [20]:

where n is the number of significant variables.