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
109^{14} mortar
cubes, making use of the gel-space ratio concept of Powers and Brownyard,^{
35} The gel-space
ratio is defined by^{35
}

(8) |

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 C_{3}A 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 *t*_{0
}, 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_{
3}A 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