Use of Design of Experiments (DoE) to Model the Sulphate Agent Amount of (Ultra)Finely Ground and Fast Hardening Portland Cement Clinker
Abstract
:1. Introduction
1.1. Fast-Hardening Cements
- (1)
- Silicate reaction of the clinker phases C3S (alite) and C2S (belite): Calcium silicate hydrates (C-S-H phases) and additional portlandite (Ca(OH)2) are formed. The hydration of the alite proceeds comparatively quickly. Although the tabular portlandite can be identified by X-ray, the C-S-H crystals on the contrary are apparently X-ray amorphous and thus can only be quantified to a limited extent by XRD analysis. High conversion of the silicate reaction stands for a high degree of hydration and high early strength.
- (2)
- Aluminate reaction at the early hydration age of the C3A (tricalcium aluminate) with the sulphate agent: Prismatic ettringite and/or tabular monosulphate crystals are formed. In the absence of a sulphate agent, C-A-H phases are formed simultaneously. However, due to the mostly low crystallinity, the variable chemism and instabilities, a qualitative determination of the tabular monosulphate and the C-A-H phases is difficult [2].
- Increase in the C3S-amount
- Increase in the C3A-amount
- Change of sulphate agent and sulphate amount
- Increasing the grinding fineness of the cement
- Use of inorganic and organic additives.
1.2. Models to Determine the Optimised SO3 Content in Dependency of Different Clinker Types
1.3. Design of Experiments (DoE)
- ❖
- A-optimality: optimisation of the mean-variance of the regression coefficients
- ❖
- G-optimality: optimisation of the max. occurring variance of the prediction values
- ❖
- V-optimality: optimisation of the mean prediction quality in the factor space.
2. Materials and Methods
2.1. Basic Mixture
- Clinker 3000 cm²/g (C3): w/b-ratio = 0.3
- Clinker 7000 cm²/g (C7): w/b-ratio = 0.35
- Clinker 12,000 cm²/g (C12): w/b-ratio = 0.45.
- Hemihydrate (7080 cm²/g Blaine)
- Anhydrite (7835 cm²/g Blaine)
- C-S-H-seeds (Circosil® 0,1 (tobermorite), Circolit® (xonotlite))
- Silica fume.
- ➢
- (clinker-fineness/1000)_(SO3[%])_(hemihydrate/anhydrite)
2.2. Analytics
2.2.1. XRD
2.2.2. ESEM
2.2.3. Ultrasonic Test
2.3. Design of Experiments
- The sulphate agent ratio was varied from 0/100–100/0 (hemihydrate/anhydrite).
- The sulphate agent amount was varied in defined steps by the choice of a prefactor concerning Equation (3). Without using a sulphate agent the mixtures did not allow processability.
- The amount of C-S-H-seeds was varied in relation to the cement content.
- The clinker meal was varied in the grinding finenesses 3000, 7000 and 12,000 cm²/g.
- The C-S-H-seeds type is divided into tobermorite- (Circosil® 0.1) and xonotlite-structure (Circolit®).
3. Results
3.1. Development of a D-Optimal Test Matrix by DoE
3.2. Analysis of the Degree of Hydration with Regard to the Silicate Phase
3.3. Analysis of the Ettringite Formation with Regard to the Aluminum Phase
3.3.1. Evaluation of Significant Factors Influencing the Ettringite Formation by DoE
3.3.2. Chemical-Mineralogical Analysis of Phase Development
- C7_4.50_25/75 (ettringite change: 138.4%; 77.3 MPa)
- C7_4.50_75/25 (ettringite change: 132.9%; 72.5 MPa).
4. Discussion and Evaluation
4.1. Modeling the Optimal SO3-Content for Clinker Meals with a High Grinding Fineness
- C3: XScontent = 1.75
- C7: XScontent = 0.50
- C12: XScontent = 0.39.
- ❖
- runs through the measured values determined using DoE
- ❖
- is monotonically decreasing in the interval I1 = [3; ∞)
- ❖
- only slowly tends towards 0 for x → +∞
- ❖
- has exclusively positive y-values in the interval I1 = [3; ∞).
- ❖
- exponential function of the form f1(x) = a∙ebx, f2(x) = b∙akx
- ❖
- power function of the form f3(x) = a∙xn (n ∈ R), which guarantees monotonicity as written above
- ❖
- fractional rational function of the form f4(x) = und f5(x) =.
- fk(3) = 1.75
- fk(7) > k(7) = 0.50
- fk(12) k(12) = 0.40 (rounded up).
- a = 0.372208
- b = 2.38462
- c = 0.064516.
4.2. Evaluation
- fcompound (Na2O, K2O, 3000, Fe2O3) = 3.35% SO3
- fcompound (Na2O, K2O, 12,000, Fe2O3) = 7.20% SO3.
5. Conclusions and Outlook
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Oxide | C3 (Clinker 3000 cm²/g) | C7 (Clinker 7000 cm²/g) | C12 (Clinker 12,000 cm²/g) |
---|---|---|---|
[wt%] | [wt%] | [wt%] | |
SiO2 | 22.00 | 20.88 | 19.77 |
Al2O3 | 5.90 | 5.59 | 5.73 |
Fe2O3 | 2.14 | 2.13 | 2.37 |
CaO | 66.94 | 65.74 | 63.85 |
MgO | 0.97 | 0.92 | 0.97 |
SO3 | 0.82 | 0.80 | 1.43 |
Na2O | 0.37 | 0.34 | 0.45 |
K2O | 0.65 | 0.66 | 1.16 |
Cl | 0.01 | 0.01 | 0.02 |
P2O5 | 0.14 | 0.14 | 0.13 |
sulphide | 0.09 | 0.10 | 0.14 |
Parameter | Value |
---|---|
Radiation | CuKα |
Voltage/Current | 40 kV/30 mA |
Angle range | 5° 2 Theta–65° 2Theta |
Step width | 0.0057 °2Theta |
Measuring time per step | 0.05 s |
Total number of steps | 10,522 |
Delay time | 47 s |
Measuring time per range | 10 min |
Divergence gap | 0.05 mm |
Factor | Type | Bottom Star Point | Lower Limit | Center Point | Higher Limit | Upper Star Point |
---|---|---|---|---|---|---|
Sulphate agent ratio | steady | 0/100 | 25/75 | 50/50 | 75/25 | 100/0 |
SO3-amount (pre-factor Ost & Lerch) | steady | 0.25 * | 0.5 * | 0.75 * | 1.0 * | 1.25 * |
C-S-H-seeds amount | steady | 0 wt% | 0.5 wt% | 1 wt% | 1.5 wt% | 2 wt% |
Fineness of clinker | categorical | 3000 cm²/g | 7000 cm²/g | 12,000 cm²/g | ||
C-S-H-seeds type | categorical | Circosil® 0.1 | Circolit® |
Clinker 3000 cm²/g | Clinker 12,000 cm²/g | ||
---|---|---|---|
C3_2.90_25/75 | 67.3 MPa | C12_6.75_25/75 | 70.7 MPa |
C3_3.35_25/75 | 71.4 MPa | C12_7.20_25/75 | 76.2 MPa |
C3_3.80_25/75 | 63.1 MPa | C12_7.65_25/75 | 72.1 MPa |
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Schade, T.; Middendorf, B. Use of Design of Experiments (DoE) to Model the Sulphate Agent Amount of (Ultra)Finely Ground and Fast Hardening Portland Cement Clinker. Materials 2021, 14, 5573. https://doi.org/10.3390/ma14195573
Schade T, Middendorf B. Use of Design of Experiments (DoE) to Model the Sulphate Agent Amount of (Ultra)Finely Ground and Fast Hardening Portland Cement Clinker. Materials. 2021; 14(19):5573. https://doi.org/10.3390/ma14195573
Chicago/Turabian StyleSchade, Tim, and Bernhard Middendorf. 2021. "Use of Design of Experiments (DoE) to Model the Sulphate Agent Amount of (Ultra)Finely Ground and Fast Hardening Portland Cement Clinker" Materials 14, no. 19: 5573. https://doi.org/10.3390/ma14195573