Model Results

Some general results of the microstructure model will first be presented, before proceeding to the calibration of model hydration rate, heat release, and chemical shrinkage against the experimental data. Results can be conveniently summarized by plotting the phase volume fraction vs. number of elapsed dissolution cycles for each phase present in the model. Typical results are illustrated in Figures 10 through 12 which provide a series of graphs for Cement 116 at w/c=0.4. For the anhydrous phases (C₃S, etc.), the phase fractions are seen to monotonically decrease with cycles, but at rates proportional to the assigned dissolution probabilities of the phase (i.e., C₃S and C₃A react at higher rates than C₂S and C₄AF). Similarly, as shown in Fig. 11, porosity decreases monotonically with cycles. C-S-H, CH and FH₃ all are seen to increase monotonically with cycles.

  

Figure 10: Model anhydrous cement volume fractions vs. elapsed cycles for Cement 116 with w/c=0.4.

  

Figure 11: Model porosity and reaction product volume fractions vs. elapsed cycles for Cement 116 with w/c=0.4.

The behavior of the aluminate hydration products is more complex as shown in Fig. 12. Here, while gypsum remains in the system at a significant level (> 10% of its initial volume), mostly ettringite (and a little C₃AH₆) is formed from the reaction of the aluminate phases with gypsum. When the gypsum is nearly consumed, the formation of the monosulfoaluminate phase (Afm) begins and the supply of ettringite is gradually depleted, while more C₃AH₆ continues to form. The initiation of monosulfoaluminate formation prior to the complete depletion of gypsum is consistent with recent experimental results [38]. The shapes of the curves for the ettringite buildup and decay and the Afm buildup are quite similar to those found in the literature [28], as measured using X-ray diffraction on pastes in which the dissolution of the ferrite phase had been specially activated. In Fig. 12, the ettringite peaks to a maximum volume fraction at about 60-70 cycles. Later results will present the calibration of model cycles against experimental time; such results indicate that 60-70 cycles corresponds to about 12-15 hours of real time for these cements. This is a reasonable time for the conversion of ettringite to monosulfoaluminate to begin, as indicated by a secondary peak in calorimetry measurements [8, 39]. Such a shoulder (peak) on the heat release curve can be clearly observed for the heat release signal curve for Cement 116 in Fig. 4 (occurring at about 750 minutes). However, some researchers [40] have suggested that this secondary heat peak is associated with the renewed formation of ettringite and not the conversion of ettringite to monosulfoaluminate. It should be recognized that model parameters could be adjusted to obtain this depletion of gypsum at any specific time. Here, the relative agreement with conventional experimental observations is rather fortuitous, as no specific attempt was made to achieve this gypsum depletion at a specific time. Rather, the relative dissolution probabilities of the phases were set a priori at reasonable values based on data in the literature [8].

  

Figure 12: Model aluminate reaction product volume fractions vs. elapsed cycles for Cement 116 with w/c=0.4.

Concerning the model heat release data, the values calculated based on the major phase enthalpies at complete hydration can be compared to those based on the tabulated heats of formation of all of the phases. Figure 13 provides a comparison of these two results for Cement 116 with w/c=0.45. The two curves are seen to overlap early in the hydration, but diverge in the later stages. This is partially an artifact of the diffusing species remaining in solution from one dissolution cycle to the next in the model, as heats of formation can be only approximately applied to these species since multiple reaction paths are possible. Late in the hydration, a small but significant quantity of diffusing ettringite and diffusing C₃A species are observed to build up in the pore space. Conversely, when using the major phase enthalpies at complete hydration, the heat release can be updated completely after each dissolution cycle, based on the amount of remaining unhydrated cement phases. Since the experimentally measured heats of hydration after 7 days are on the order of 300 kJ/kg, it is somewhat difficult to say which of the two model curves in Fig. 13 best represents the experimental data. However, based on the differences in heats of hydration after 7 and 28 days measured using the heat of solution technique [5], the model values based on the major phase enthalpies do provide a better agreement with the experimental data.

  

Figure 13: Comparison of heat release via major phase enthalpies and heats of formation for Cement 116 with w/c=0.45.