Discussion

The previous results indicate that quantitative characterization of the initial cement powder can lead to the successful prediction of a variety of performance-related phenomena associated with cement hydration such as heat release and chemical shrinkage. However, at present, few laboratories have the capability of performing the SEM/X-ray analysis presented in the experimental section. With this in mind, further modelling was executed based solely on the measured particle size distributions of the cements and the Bogue-calculated potential phase compositions. For both cements being studied, starting microstructures with monophase cement particles following the measured PSD and Bogue phase fractions were created for w/c=0.40. Thus, for each particle placed in the three-dimensional volume, the phase assigned to the particle was selected based on the relative volume fractions of the phases. The same cement hydration and microstructure program was then executed to model hydration behavior and the regression analysis performed to relate model cycles to real time as described previously.

The results for these monophase particle cements are provided at the end of Appendix B. While the model follows the experimental data at early times, significant divergence occurs at longer times (seen most clearly on the degree of hydration plots). In addition, for Cement 116, the model heat release and chemical shrinkage curves are seen to differ significantly from their experimental counterparts, more so than when multi-phase cement particles are used in the model (compare Figs. 42 and 43 to Figs. 33 and 34). One would expect the actual distribution of phases in the cement particles to have a greater influence at longer times, as depending on the distribution, certain phases may become totally surrounded by hydration products and be unavailable for further hydration. Recognizing that only two cements have been explored, while cement particle size distribution is certainly critical to the observed hydration kinetics, actual phase volume fractions and spatial distributions within particles also appear to be important for accurately modelling the performance of real cements at times exceeding several days.

In terms of performance variables, one key property is the compressive strength. In this study, we have also attempted to predict the compressive strength development of standard ASTM C109 [6] mortars cubes, making use of the gel-space ratio concept of Powers and Brownyard. The gel-space ratio is defined by [24]:

$$X=\frac{0.68\alpha}{0.32\alpha+(w/c)}.$$ (10)

It has been shown that the compressive strength of ASTM C109 mortar cubes, $\sigma_c$_c , can be related to this gel-space ratio in the following manner [24]:

$$\sigma_c=AX^n$$ (11)

where A represents the intrinsic strength of the cement and n takes on values between 2.6 and 3.0, depending on the cement being investigated. Powers and Brownyard observed the value of A to be lower for cements with higher Bogue potential C₃A contents (e.g., > 7%). Recently, Radjy and Vunic [43] have shown that the gel-space ratio can be employed to predict the compressive strength development of concrete based on measuring the adiabatic heat signature to estimate the degree of hydration.

Based on ASTM C109 [6], test mortars are prepared with w/c=0.485 for portland cement materials. Thus, model cements with w/c=0.485 were generated for Cements 115 and 116 using the previously described computational techniques. Since no experimental non-evaporable water content data were available, the values of t₀ and B determined for each of the two cements at w/c=0.45 were used to convert model cycles to time based on Equation 9. From the CCRL test program, compressive strengths at 3, 7, and 28 days were available. The cement hydration and microstructure program was utilized to compute the expected degree of hydration, $\alpha$, for these cements at 3, 7, and 28 days, so that X could be computed according to Equation 10. The 3-day measured compressive strength was then used to determine the value of A in Equation 11, assuming an exponent n of 2.6. Values of A of 129 and 99 MPa were thus determined for Cements 115 and 116, respectively. As noted above, Cement 116, with the higher C₃A content, is observed to have the lower intrinsic strength.

Once A was determined, the model could be used to predict $\sigma_c$ _c at 7 and 28 days for comparison to the experimental data. Figures 14 and 15 present the predicted strength developments in comparison to those measured in the CCRL proficiency sample program. The standard deviation in the measured values is also included in the plots for reference purposes. The predictive ability of the model is again demonstrated, as it appears that compressive strength can be predicted well within the standard deviation of an interlaboratory test program.

  

Figure 14: Predicted and measured compressive strength development for Cement 115.

  

Figure 15: Predicted and measured compressive strength development for Cement 116.

The reproducibility of results of the computer model was investigated in two ways. First, given a starting microstructure (Cement 116 with w/c=0.4), the 3-D hydration model was executed with three different random number seeds. As can be seen in Fig. 44 in Appendix C, the variability is totally negligible as it is not possible to distinguish the three different degree of hydration curves one from another. In the second case, three different random starting microstructures were generated for Cement 116 with w/c=0.4. Then, the hydration model was executed on each using the same starting random number seed. Once again, the variability observed in Fig. 45 in Appendix C is seen to be minimal. Thus, matching experimental results to a single execution of the model seems reasonable for calibration purposes.

These results are preliminary in nature as only two cements at room temperature have been studied. However, the results are encouraging, with good agreement between model and experimental results. Ongoing experimental studies are extending the research to two other temperatures (15 and 35^oC) so that an Arrhenius-type model for representing the hydration of cements over a range of temperatures may be investigated. Thus, the coefficients in the parabolic dispersion model of Knudsen will be written as functions of temperature using the Arrhenius equation or an alternative [35]. The model already includes the information necessary for incorporating silica fume into cement-based materials. Here, it will be necessary to calibrate the relative rate of the pozzolanic reaction to that of CH dissolution/precipitation to properly model the observed build up and decay of solid CH volume with time [44]. Preliminary studies have shown that this type of behavior can be achieved in the monophase C₃S model system.