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6. Example Results

Comparison of Experimental Techniques for Quantifying Hydration

Figure 11. Experimental results for CCRL Cements and 115 and 116 vs. time.

One interesting observation can be made concerning the chemical shrinkage data for the lower w/c ratios in Fig. 11. For both the 0.3 and 0.4 w/c ratios, one can observe that at longer times, the chemical shrinkage curves diverge away from the non-evaporable water content data. In every case, the chemical shrinkage is seen to lie below the non-evaporable water data at these long times. As has been suggested by Geiker [33], this is due to the depercolation of the capillary porosity in the hydrating cement paste. As hydration occurs, depending on the initial w/c ratio, a point will be reached where the capillary porosity is no longer connected, and transport must then occur through the much smaller gel pores in the C-S-H gel [7]. Since this transport will occur at a much slower rate, the rate at which water is absorbed into the specimen will fall below the rate at which empty voids are being generated, leading to the observed divergence in the experimental curves. The horizontal lines provided in Fig. 11 indicate the degree of hydration needed to achieve this capillary pore discontinuity, based on the results of the original C3S hydration model [7, 9]. The agreement between the experimental observations and the predicted point of discontinuity is quite good, particularly for the w/c=0.3 data sets.

Fitting of Experimental Degree of Hydration vs. Time Data

To calibrate the model to the experimental results, both are fitted to the same functional form. In the literature, a variety of models have been used to fit either degree of hydration or strength development vs. time [37], mainly in connection with the application of the maturity method to concrete strength development. Two commonly used models are the linear and parabolic dispersion models originally developed by Knudsen [38]. The parabolic form of the model, which was found to generally provide the better fit to the experimental data [10], takes the form:

It should be noted that this equation does not attempt to model the early acceleratory period of the cement hydration (0 to 0.15), but generally provides an excellent fit to experimental data for degrees of hydration greater than 15% [38]. Equation 6 was fitted to the experimental non-evaporable water content data using non-linear regression analysis available in DATAPLOT [39], a graphical analysis software package developed at NIST. While the 8-hour data point for non-evaporable water content, generally corresponding to a degree of hydration of 10-15%, is slightly outside the range of application of the dispersion model recommended by Knudsen [38], the fitted lines deviated little from these datum values, suggesting that degrees of hydration greater than 0.10 may be a more practical application range for equation 6. Figure 12 provides a representative example of the fit of the Equation 6 to the experimental data; for both cements, the fits in general were excellent. Table 3 summarizes the results of the regression analysis, including the results generated at all three temperatures investigated in this study. For the 25 C results, the value of t_o is seen to be relatively constant for a given cement at the three different w/c ratios.

Figure 12. Fit of Knudsen's parabolic dispersion model to experimental non-evaporable water content (g H₂O/g cement) vs. time for Cement 115 with w/c=0.4 and T=25 C.

Effects of Temperature

Table 3 also contains the values of A_u, k, and t_o determined via the non-evaporable water content measurements at 15 C and 35 C. As would be expected, the rate constant, k, is seen to be a strong function of temperature. In addition, the induction period, t_o, is seen to decrease slightly with increasing temperature, as does the value of A_u, the asymptotic non-evaporable water content. Geiker [33] has noted a similar trend for the values of A_u, quoting values of 0.206, 0.201, and 0.198 g H₂O/g cement for curing temperatures of 20 C, 35 C, and 50 C, respectively, for a rapid hardening portland cement with w/c=0.45, based on the data of Munkholt [40]. Perhaps the simplest method for relating model results calibrated at 25 C to other temperatures is through the use of a maturity-type approach [37, 41]. Here, an Arrhenius function of the form:

Using the average value of the activation energies given in Table 4, 38.2 kJ/mole, multiplicative factors of 0.585 and 1.65 would be necessary to convert the curing times at 15 C and 35 C to equivalent times at 25 C, respectively. Using these two values and correcting the time at each temperature by first subtracting off the induction time determined for each temperature and w/c ratio, as given in Table 3, Figure 13 provides plots of the degree of hydration, estimated via the non-evaporable water content, vs. time for the two cements and three w/c ratios. In every case, using the equivalent time concept collapses the three data sets onto a single master curve. While some dispersion is seen at longer times, in general, the three data sets asymptote to about the same value for degree of hydration, for a fixed cement and w/c ratio.

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Figure 13. Superposition of degree of hydration results at three temperatures for CCRL Cements 115 and 116.

Model Results

Some general results of the microstructure model will first be presented, before proceeding to the comparison of model hydration rate, heat release, and chemical shrinkage to 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 14 through 16 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. 15, porosity decreases monotonically with cycles. C-S-H, CH and FH₃ all are seen to increase monotonically with cycles.

Figure 14.Model anhydrous cement volume fractions vs. elapsed cycles for Cement 116 with w/c=0.4.

Figure 15. 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. 16 for the first 800 cycles of hydration. 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 on the pure aluminate phases [42]. The shapes of the curves for the ettringite buildup and decay and the Afm buildup are quite similar to those found in the literature [27], as measured using X-ray diffraction on pastes in which the dissolution of the ferrite phase had been specially activated. The persistence of ettringite at long times is also consistent with the recent synchrotron radiation-energy dispersive diffraction measurements of Henderson et al. [43], who measured ettringite contents on the order of 7% after 326 days of hydration for a w/c=0.5. This value is larger than those predicted by the model in the present study, which could be due in part to the lower sulfate content of the cements (about 1.6% SO₃ vs. the 2.7-2.9% in Table 1) used in [43].

Figure 16. Model aluminate reaction product volume fractions vs. elapsed cycles for Cement 116 with w/c=0.4.

Calibration of Experimental to Model Predictions

To fit the model results to those measured experimentally, a conversion between cycles and time is necessary. The following conversion between time and cycles has been found to provide very reasonable fits to the experimental data:

To calibrate the model to the experimental results based on the non-evaporable water content data, the model results for degree of hydration were regressed in Knudsen's parabolic dispersion equation using the earlier deduced parameters for A_u and k, and a subset of the model degree of hydration data. This subset was generated by selecting single data points at approximately 0.05 degree of hydration intervals for values of degree of hydration between 0.10 and the amount of hydration achieved experimentally at 90 days. In this way, the regression being applied to the model is being weighted in approximately the same manner as that which was applied to the experimental results. This step was deemed necessary due to the fact that the model degree of hydration values are not evenly distributed with number of cycles (i.e., more hydration occurs during the early cycles than during the later ones). The previously determined value of A_u was converted to a degree of hydration, via normalization by the value for the non-evaporable water content at complete hydration (0.226 or 0.235) [10].

The coefficients determined for B as a function of cement and w/c ratio are summarized in Table 5. Interestingly, the values for B are relatively constant, suggesting that a constant value of B (such as the average B value of 0.0017) can serve to model all of the results for the two cements and three w/c ratios. From the variability in results in Table 3, an average value of t_o (namely 6.7 hours) may also suffice for these two particular cements at 25 C. This value is slightly larger than the final times of set measured for the two cements using the Vicat and Gillmore needle techniques [45], which are both on the order of 5 hours [46].

Once a value(s) of B has been determined, plots comparing model and experimental results can be generated. Figures 17 through 19 provide example fits of the model to the experimental data for cement 115 with w/c=0.4. In these figures, the solid lines indicate the model data obtained using the specific values of t₀ and B for w/c=0.4 for cement 115 as given in Tables 3 and 5, while the dotted lines indicate the results that would be obtained using single average values for these parameters regardless of w/c ratio and cement ID. As can be seen in the three figures, the agreement between the solid lines and the experimental data is in general excellent. For the other w/c ratios and for cement 116, the quality of the fits was similar to that exhibited in Figures 17 through 19 [10]. For the dotted lines, the agreement is similar, suggesting that for these two cements, a single relationship can be used to convert model cycles into real time. This suggests that, by capturing the particle size distribution and phase distributions of the cements, much of the hydration kinetics behavior is implicitly included in the hydration model, i.e., the initial cement particle microstructure has a large influence on the post-induction period kinetics of cement hydration. Thus, a calibration performed for one cement at one w/c ratio can be used to predict the hydration behavior of other cements, of reasonably similar phase composition, at a variety of w/c ratios.

Figure 17. Measured and model degree of hydration vs. time for Cement 115 with w/c=0.4.

Figure 18. Measured and model chemical shrinkage vs. time for Cement 115 with w/c=0.4.

Figure 19. Measured and model heat release vs. time for Cement 115 with w/c=0.4.

Effects of Sealed Hydration

In addition to temperature, another material environmental condition variable of interest in hydration studies is the moisture content of the cement paste. Because cement hydration is generally viewed as a dissolution/precipitation process, the availability of water in the capillary pore space is paramount. As indicated by the chemical shrinkage measurements presented above, in a sealed system, empty pores will be created as the hydration proceeds. This in turn would be expected to affect the kinetics of the hydration due to changes in solution concentrations and the reduction in available volume into which reaction products can precipitate. Modelling of this behavior will be especially important for high performance concretes, which are often based on mixture proportions with w/c less than about 0.35, not only due to the expected reduction in hydration (and strength) relative to saturated curing, but also because the meniscii created as the pores empty will induce drying (self-desiccation) shrinkage stresses within the microstructure [47], even before the material's strength is fully developed.

To preliminarily test the capability of the NIST cement hydration model to effectively reproduce the effects of self-desiccation on hydration kinetics, the model was executed for Cement 115 with w/c=0.3 under conditions in which no external water was available, so that empty pores were created as the hydration proceeded as described in Section 4. In addition, experimental measurements were made under both saturated and sealed conditions. Figure 20 provides a comparison of the experimental measurements and model predictions for degree of hydration vs. time for these two systems. Model cycles were converted to time using values of B=0.0017 and t_o=6.7. Once again, the model is found to reproduce the experimentally-observed difference in hydration kinetics due to the self-desiccating conditions. Early in the hydration process, the kinetics are not strongly influenced as sufficient water is present and few empty pores exist. However, as hydration continues, the empty pores occupy an ever increasing fraction of the remaining total porosity, resulting in a significant decrease in achieved degree of hydration. This can be seen clearly in Figure 21, which compares two-dimensional slices from the same z-plane after 5000 cycles of hydration under both saturated and sealed conditions. If an accurate model could be developed for the drying kinetics of a hydrating cement paste, it should be possible to extend the cement hydration model to consider hydration of cement paste exposed to different external relative humidities, in addition to the saturated and sealed conditions explored in this study.

Figure 20. Predicted and measured degrees of hydration for Cement 115 with w/c=0.3 hydrated under sealed and saturated conditions at 25 C.

Figure 21. Comparison of hydrated microstructures for hydration under saturated (left) and sealed (right) conditions. C₃S is red, C₂S is aqua, C₃A is green, C₄AF is orange, gypsum is pale green, C-S-H is yellow, other hydration products are magenta, water-filled porosity is blue, and empty porosity is black.

Prediction of Compressive Strength

In terms of performance variables, one key property is the compressive strength. Previously, Osbaeck and Johansen [48] have developed a mathematical model relating cement particle size distribution to strength development. Assuming that the depth of the hydrated layer is independent of particle diameter (which is also tacitly assumed in the NIST cement hydration model) and proportional to the square root of time, they were able to quantitatively predict the effects of particle size distribution on strength evolution. More recently, Tsivilis and Parissakis [49] have also shown that cement fineness is a key factor influencing compressive strength, with phase compositions becoming significant at later ages. In this study, we have also attempted to predict the compressive strength development of standard ASTM C109 [45] mortars cubes, making use of the gel-space ratio concept of Powers and Brownyard. The gel-space ratio is defined by [23]:

where S_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 S_a to be lower for cements with higher Bogue potential C₃A contents (e.g., > 7%) [23]. Recently, Radjy and Vunic [50] 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 [45], 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 t_o and B determined for each of the two cements at w/c=0.45 were used to convert model cycles to time. From the CCRL test program, compressive strengths at 3, 7, and 28 days were available. The NIST cement hydration model was utilized to compute the expected degree of hydration for these cements at 3, 7, and 28 days, so that X could be computed according to the above equation. The 3-day measured compressive strength was then used to determine the value of S_a, assuming an exponent n of 2.6. Values of S_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 S_a was determined, the model could be used to predict S_c at 7 and 28 days for comparison to the experimental data. Figure 22 presents the predicted strength developments in comparison to those measured in the CCRL proficiency sample program [46]. 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. Since the model accounts explicitly for the particle size distribution and phase composition of a cement, these results suggest that these parameters effect strength mainly through their influence on the hydration kinetics of the cement paste, as the equations given above are based solely on the degree of hydration and the w/c ratio of the system.

Cement 115

Cement 116

Figure 22. Predicted and measured compressive strength development for Cements 115 and 116.