4.1 Later age materials

Two different cements were chosen to test whether the combination of CEMHYD3D and finite element computations could accurately predict cement paste elastic moduli at later ages. The first cement was denoted D, and was roughly equivalent to an ASTM Type I cement. Its composition is given in Table 2 in terms of the major chemical phases present in the cement. This was a finely ground cement, thus showing fast early hydration. The cement particle size distribution (PSD), phase abundance in the cement powder, and amount and forms of gypsum were analyzed so that CEMHYD3D could accurately hydrate this cement and make hydrated microstructures. It is interesting to note that in this cement, the gypsum (volume fraction of 5 % of the cement) was mainly in the form of anhydrite (2/3), and hemihydrate (1/3), probably in order to guarantee an optimized strength development. The cement also included a volume fraction of about 5 % inert filler, mainly limestone. A second cement, ASTM Type I, was denoted H. It was somewhat different chemically from the D cement, as seen in Table 2, and was somewhat coarser. Figure 2 shows the PSD curves of both cements, displaying the differences in PSD between them. Table 2 and Fig. 2 also show the chemical phase information and PSD, respectively, for a third cement, denoted L, which will be discussed later in Section 4.2. All three cements were analyzed and incorporated into the Virtual Cement and Concrete Testing Laboratory (VCCTL) database, so that microstructures could be generated.

Table 2: Chemical phase composition of the three cements used in this paper (unit is volume fraction of total cement). Estimated uncertainty in each number is approximately 5 %.

Figure 2: Cumulative (volume-based) particle size distributions for D, H, and L cements.

Figure 3 shows the experimental degree of hydration vs. w/c ratio, measured using non-evaporable water content, for 28 d and 56 d periods of saturated hydration for the D cement and for 14 d and 56 d periods of saturated curing for the H cement. Non-evaporable water content is essentially the mass loss between 105 ºC and 1000 ºC, which can be used to give a measure of the degree of hydration [7]. These values are an average over three specimens, with an uncertainty ranging from 0.5 % to 2.1 %. Note that the degree of hydration is higher for the D cement, almost certainly due to the finer particle size. For all systems studied, the degree of hydration was above 50 %, although full hydration was not achieved at 56 d. The CEMHYD3D [7] model was run until the model degree of hydration closely matched the experimental degrees of hydration. Then these microstructures were saved for elastic moduli computation.

Figure 3: Degree of hydration vs. w/c for 28 d and 56 d results on D cement and 14 d and 56 d results for H cement.

Figure 4 shows cross-sections of the 56 d cement D simulated microstructures. Hydration is nearly complete after 56 d. The low w/c ratio pastes are characterized by large amounts of unhydrated clinker phases and very low porosity, while the higher w/c ratio pastes have higher amounts of porosity and almost no clinker phases leftover. So we could say that the low w/c pastes are C-S-H/CH composites reinforced by the stiff clinker phases, while the higher w/c ratio pastes are C-S-H/Ch composites made less stiff by pore inclusions. Also, in the lower w/c value microstructures, there is some hint of the original spherical particle shape left for the largest cement particles. Recent CEMHYD3D model improvements have allowed real cement particle shapes to be used in the starting particle microstructure [9]. In composite materials, it is well known that the shape of the phases can play a large role in determining the overall properties, including elastic behavior [41-43]. Examining the cement paste model microstructures of the H and D cements above revealed that due to cement consumption during hydration, initial cement particle shape would not have played much of a role in the elastic properties of these cement paste systems. However, the remnant spherical particle shapes in the lower w/c pastes imply that there could be a small effect of particle shape even at this late stage of hydration. It is probably true, though, that cement particle shape could play a very large role in determining early-age mechanical behavior, as the cement particles will play the role of relatively very stiff inclusions in a quite soft matrix. It is known that the higher the contrast between inclusion and matrix, the more effect the shape of the inclusion has upon composite properties [41-43]. This will be discussed more in the next section.

Figure 4: 56 d D cement paste microstructures (Top row, starting from left: w/c = 0.25, 0.3, 0.35, 0.4; second row, starting from left: w/c = 0.45, 0.5, 0.55, 0.6). White is the unreacted cement particles, black is pore space, and all hydration products are gray.

Figure 5 shows the experimental and model results for E and G for the D cement, plotted vs. w/c ratio. The experimental results for both cements were obtained via elastic resonance measurements (similar to ASTM E1875-00e1 Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Sonic Resonance). In these experiments, E and G were measured directly, so that the model results are presented for the same two parameters. The experimental results are an average over three specimens, with an uncertainty between 0.5 % and 0.8 %. At each w/c value, the lower value is the 28 d result and the upper value is the 56 d result. There is excellent agreement between model predictions and experimental results, mostly within 5 % although up to 10 % disagreement for some values. The cement paste microstructure is isotropic on average, and so a pure shear and hydrostatic compression can be applied at the same time, since any cross terms in the elastic moduli tensor, e.g. C₁₁₂₃, are small compared to the other components within numerical round-off error, and average to zero.

Figure 5: D cement data, 28 d and 56 d results. At each w/c value, the 28 d and 56 d elastic moduli values make the curves seem jagged. The 56 d values are always higher than the 28 d values.

In Fig. 6, the model and experimental results are plotted for (a) 14 d of curing and (b) 56 d of curing for the H cement. The format of the graph is similar to that of Fig. 5, and the experimental uncertainties were similar. The same excellent agreement between experiment and model is demonstrated. At the highest w/c value, some bleeding was noted, which tended to raise the measured elastic moduli values. The model was run for a slightly lower w/c ratio, 0.55 instead of 0.6, and good agreement was obtained for the 0.6 w/c point.

Figure 6: H cement data. (a) 14 d, (b) 56d