In terms of performance variables, one important property is the compressive strength. Previously, Osbaeck and Johansen 58 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 also is assumed tacitly 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 59 also showed that cement fineness is an important factor influencing compressive strength, with phase compositions becoming significant at later ages. In this study, we also have attempted to predict the compressive strength development of standard ASTM C 10914 mortar cubes, making use of the gel-space ratio concept of Powers and Brownyard, 35 The gel-space ratio is defined by35
where is the degree of hydration.
Interactive graph for equation follows:
It has been shown that the compressive strength of ASTM C 109 mortar cubes (c,) at any age (t) can be related to this gel-space ratio in the following manner: 35
|c ( t ) = A X ( t ) n||(9)|
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%). 35 Recently, Radjy and Vunic 60 showed that the gel-space ratio can be used to predict the compressive strength development of concrete based on measuring the adiabatic heat signature to estimate the degree of hydration.
Based on ASTM C 109, 21 test mortars were 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. Because no experimental nonevaporable 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 Eq. (7). From the CCRL test program, compressive strengths at 3, 7, and 28 d were available. The NIST cement hydration model was utilized to compute the expected degree of hydration for these cements at 3, 7, and 28 d, so that X could be computed according to Eq. (8) . The 3 d measured compressive strength then was used to determine the value of A in Eq. (9), 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 C 3A content, was observed to have the lower intrinsic strength.
Once A was determined, the model could be used to predict c , at 7 and 28 d for comparison to the experimental data. Figure 15 presents the predicted strength developments in comparison to those measured in the CCRL proficiency sample program. 20 The standard deviation in the measured values also is included in the plots for reference purposes. The predictive ability of the model again is demonstrated, because it appears that compressive strength can be predicted well within the standard deviation of an interlaboratory test program. Because the model explicitly accounts for the particle-size distribution and phase composition of a cement, these results suggest that these parameters affect strength mainly through their influence on the hydration kinetics of the cement paste, because Eqs. (8) and (9) are based only on the degree of hydration and w/c ratio of the system.
Fig. 15 Predicted and measured compressive strength development for Cements 115 and 116