Chemical shrinkage can be directly measured using either a gravimetric 5, 8 or a volumetric method.5, 9, 10 While no standard U.S. method exists for evaluating chemical shrinkage (one does exist in Japan 11), the test is relatively simple and is currently under consideration by the ASTM C01.31 Volume Change subcommittee. Since data on the long term chemical shrinkage is desirable for the internal curing calculation, an alternative to measurement is to calculate it based on the phase composition of the cement.
Knowing the molar volumes of all relevant cement phases (as provided in Table I)9, 12, 13 and the expected cement hydration reactions,9, 14 the chemical shrinkage due to the hydration of each of the principal cement clinker phases can be calculated.8 Typical coefficients (per unit mass of cement clinker phase) are provided in Table II. For the aluminate phases, the exact value depends strongly on the sulfate content of the cement and the resulting balance between the formation of ettringite (high sulfate content) and the monosulfoaluminate phase (lower sulfate content).
Table I.
Densities and Molar Volumes of Cementitious Materials at 25 ºC [*]|
Phase |
Density (Mg/m3) |
Molar Volume (cm3/mole) |
|
C3S |
3.21 |
71.1 |
|
C2S |
3.28 |
52.5 |
|
C3A |
3.03 |
89.1 |
|
C4AF |
3.73 |
130.3 |
|
Gypsum (dihydrate) |
2.32 |
74.21 |
|
Hemihydrate |
2.74 |
52.97 |
|
Anhydrite |
2.61 |
52.16 |
|
Silica fume |
2.22 |
27. |
|
CH (portlandite) |
2.24 |
33.08 |
|
C1.7SH4.0 |
2.11 |
107.8 |
|
C3AH6 |
2.52 |
150.12 |
|
C6AS3H32 (ettringite) |
1.7 |
735. |
|
C4ASH12 |
1.99 |
312.8 |
|
FH3 |
3.0 |
69.8 |
|
H (water) |
0.9971 |
18.07 |
It should be pointed out that these coefficients are strongly sensitive to the values chosen for the densities of the different phases in Table I, and other authors have thus calculated values different from those in Table II. 8, 15 The values given here, though, are those historically and currently used in the Virtual Cement and Concrete Testing Laboratory (VCCTL) system, whose prediction of measured chemical shrinkage has been verified on a wide variety of portland cements.9, 10, 16
Table II.
Calculated Coefficients for Chemical Shrinkage due to Cement Hydration|
Phase |
Coefficient (g water/g solid) |
|
C3S |
0.0704 |
|
C2S |
0.0724 |
|
C3A |
0.171A
0.115B |
|
C4AF |
0.117A 0.086B |
|
Silica fume |
0.20 |
AAssuming sufficient sulfate to convert all of the aluminate phases to Aft (ettringite)
B Assuming total conversion of the aluminate phases to Afm (monosulfate)
Knowing the mass composition of the cement and the chemical shrinkage coefficients in Table II, one can calculate the expected chemical shrinkage of any given portland cement. Table IIII illustrates the results of applying this calculation procedure to two recent Cement and Concrete Reference Laboratory (CCRL) proficiency cement samples. 17, 18 There is about a 10 % difference in the calculated chemical shrinkage for these two cements.
Table III
- Calculated Chemical Shrinkages for CCRL Proficiency Cement Samples|
|
Phase Mass Fractions (via SEM imaging) |
|
|
Phase |
CCRL 135 |
CCRL 140 |
|
C3S |
0.616 |
0.595 |
|
C2S |
0.160 |
0.167 |
|
C3A |
0.0604 |
0.0852 |
|
C4AF |
0.0887 |
0.0664 |
|
Chemical Shrinkage (g water/g cement) |
0.0695B |
0.0763A |
A further complication is the expected curing temperature. Geiker5 first observed that the ultimate chemical shrinkage is significantly reduced at elevated curing temperatures. The observed magnitude of this effect was on the order of 0.0005 (g water/g cement) per degree Celsius in the temperature range of 12 ºC to 50 ºC.5 For comparison, data for chemical shrinkage vs. degree of hydration at temperatures between 10 ºC and 50 ºC presented by Mounanga et al.8 yield a coefficient of approximately 0.0008 (g water/g cement) per degree Celsius. Accepting the values given in Tables I-III as being those for a nominal curing temperature of 25 ºC and taking a conservative approach to the influence of temperature, calculated values for chemical shrinkage (such as those in Table III) should be reduced by 0.005 g water/g cement for each 10 ºC that the average expected curing temperature is above 25 ºC. Conversely, they should be increased by 0.005 g water/g cement for each 10 ºC that the average curing temperature is below 25 ºC. With curing temperatures in the range of 55ºC to 35 ºC, the magnitude of this effect is on the order of 25 %. For steam curing and larger field structures (where temperatures can reach up to 60 ºC), the effect would be even more significant.