Rheological Optimization of 3D-Printed Cementitious Materials Using Response Surface Methodology
Abstract
1. Introduction
2. Materials and Methods
2.1. Raw Materials
2.2. Test Methods
2.2.1. Rheological Test
2.2.2. Flowability Test
2.2.3. Preparation Procedures
- (1)
- Dry mixing was achieved by mixing the pre-weighed cement, silica fume, slag powder, and sand in a planetary mixer for 180 s to homogenize the binder components.
- (2)
- The chemical admixtures and 75% of the total water were then slowly introduced into the dry mixture and wet-mixed for 120 s, to ensure even dispersion.
- (3)
- Water adjustment was then performed, where the remaining 25% of water was incrementally added during a 60 s mixing cycle to optimize the rheology and batch consistency.
- (4)
- Fibers were then integrated by manually feeding the fibers into the matrix and blending for 120 s to ensure uniform distribution, after which mixing was stopped to minimize fiber breakage.
2.3. Test Program
2.3.1. Response Surface Method Test Design
Single-Factor Experiment
- (1)
- Effect of the accelerator on rheological properties
- (2)
- Effect of HPMC on the rheological properties
- (3)
- Effect of PCE on the rheological properties
The Experimental Design of Response Surface Optimization
2.3.2. Three-Dimensional Printing Experiment Design
3D Printer Parameter Settings
Print Path Diagram
3. Results and Discussion
3.1. Single-Factor Test Results
- (1)
- Effect of accelerator on the rheological properties
- (2)
- Effect of HPMC solution on the rheological properties
- Effect of PCE on rheological properties
3.2. Response Surface Results
3.2.1. Response Surface Regression Model Analysis
3.2.2. Response Surface Analysis
3.3. Response Surface Results Optimization and Verification
4. Conclusions
4.1. Main Conclusions
- (1)
- Model validity was established, where a statistical analysis of the quadratic polynomials for flowability and dynamic yield stress confirmed a high goodness-of-fit (R2 > 0.95) and robust predictive accuracy across responses.
- (2)
- Factor significance
- (3)
- Flowability followed the order of polycarboxylate superplasticizer (PCE) > accelerator > hydroxypropyl methylcellulose (HPMC) solution, with significant interaction between HPMC and PCE. Dynamic yield stress followed the order of PCE > accelerator > HPMC solution.
- (4)
- The optimal mix consisted of accelerator dosage = 0.32%, HPMC solution = 0.24%, and PCE dosage = 0.23%. The experimental results showed 147.5 mm flowability (4.1% deviation) and 711 Pa dynamic yield stress (7.6% deviation), aligning closely with the predictions.
4.2. Suggestions and Prospects
- (1)
- This study only uses flowability and dynamic yield stress to judge printability, but it does not consider other important factors like thixotropy, how well layers stick together, or how long the material stays workable (open time). Focusing on just two factors may miss the other key points needed for successful 3D printing.
- (2)
- The printing tests used only one optimized mix and did not try different shapes or printing conditions. Testing more types of prints would make the results stronger and more widely useful.
- (3)
- All tests were performed in a laboratory environment using limited material quantities, and the RSM model was based on some simplifying assumptions. Therefore, the applicability of the findings in actual 3D printing or construction projects requires further validation through field-based continuous printing and long-term structural performance monitoring.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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CaO | SiO2 | Al2O3 | Fe2O3 | MgO | SO3 | K2O | Na2O | Loss | |
---|---|---|---|---|---|---|---|---|---|
C | 64.00 | 20.10 | 5.55 | 2.55 | 2.37 | 3.86 | 0.66 | 0.25 | 3.50 |
SF | 1.05 | 94.91 | 0.78 | 0.45 | 0.56 | 0.57 | 0.66 | 0.50 | 0.52 |
GS | 37.92 | 31.38 | 13.77 | 9.82 | 1.09 | 0.07 | 1.52 | 0.33 | 0.23 |
Length (mm) | Diameter (mm) | Young’s Modulus (GPa) | Elastic Modulus (GPa) | Tensile Strength (MPa) | |
---|---|---|---|---|---|
PPF | 6 | 0.02 | 13.2 | 3-5 | >480 |
Factor | Level | ||
---|---|---|---|
−1 | 0 | 1 | |
A | 0.3 | 0.4 | 0.5 |
B | 0.19 | 0.23 | 0.27 |
C | 0.2 | 0.25 | 0.3 |
No. | A Accelerator (%) | B HPMC (%) | C PCE (%) | Flowability (mm) | Dynamic Yield Stress (Pa) |
---|---|---|---|---|---|
1 | 0.3 | 0.19 | 0.25 | 155 | 751.6 |
2 | 0.5 | 0.19 | 0.25 | 152 | 765.7 |
3 | 0.3 | 0.27 | 0.25 | 153 | 651.6 |
4 | 0.5 | 0.27 | 0.25 | 150.5 | 662.2 |
5 | 0.3 | 0.23 | 0.2 | 147 | 999.9 |
6 | 0.5 | 0.23 | 0.2 | 135 | 950.6 |
7 | 0.3 | 0.23 | 0.3 | 170 | 320.2 |
8 | 0.5 | 0.23 | 0.3 | 162.5 | 355 |
9 | 0.4 | 0.19 | 0.2 | 134 | 1183.3 |
10 | 0.4 | 0.27 | 0.2 | 130 | 1111.6 |
11 | 0.4 | 0.19 | 0.3 | 160 | 233.9 |
12 | 0.4 | 0.27 | 0.3 | 160 | 200 |
13 | 0.4 | 0.23 | 0.25 | 157 | 592.1 |
14 | 0.4 | 0.23 | 0.25 | 155 | 698.5 |
15 | 0.4 | 0.23 | 0.25 | 156 | 623.2 |
16 | 0.4 | 0.23 | 0.25 | 158 | 605.4 |
17 | 0.4 | 0.23 | 0.25 | 155 | 612.8 |
Source | Sum of Squares | df | Mean Square | F-Value | p-Value | |
---|---|---|---|---|---|---|
Model | 1754.27 | 9 | 194.92 | 38.86 | <0.0001 | significant |
A | 78.12 | 1 | 78.12 | 15.57 | 0.0056 | |
B | 7.03 | 1 | 7.03 | 1.40 | 0.2751 | |
C | 1417.78 | 1 | 1417.78 | 282.65 | <0.0001 | |
AB | 0.0625 | 1 | 0.0625 | 0.0125 | 0.9143 | |
AC | 5.06 | 1 | 5.06 | 1.01 | 0.3485 | |
BC | 4.00 | 1 | 4.00 | 0.7974 | 0.0415 | |
A2 | 17.27 | 1 | 17.27 | 3.44 | 0.1059 | |
B2 | 132.04 | 1 | 132.04 | 26.32 | 0.0014 | |
C2 | 89.09 | 1 | 89.09 | 17.76 | 0.0040 | |
Residual | 35.11 | 7 | 5.02 | |||
Lack of Fit | 28.31 | 3 | 9.44 | 5.55 | 0.0656 | not significant |
Pure Error | 6.80 | 4 | 1.70 | |||
Cor Total | 1789.38 | 16 | ||||
R2 | 0.9804 | |||||
R2Adj | 0.9551 | |||||
R2pred | 0.7409 |
Source | Sum of Squares | df | Mean Square | F-Value | p-Value | |
---|---|---|---|---|---|---|
Model | 1.100 × 106 | 9 | 1.222 × 105 | 39.90 | <0.0001 | Significant |
A | 16,616.65 | 1 | 16,616.65 | 5.42 | 0.0527 | |
B | 8437.00 | 1 | 8437.00 | 2.75 | 0.1410 | |
C | 1.027 × 106 | 1 | 1.027 × 106 | 335.25 | <0.0001 | |
AB | 28.09 | 1 | 28.09 | 0.0092 | 0.9264 | |
AC | 552.25 | 1 | 552.25 | 0.1803 | 0.6839 | |
BC | 1823.29 | 1 | 1823.29 | 0.5952 | 0.4657 | |
A2 | 23,041.27 | 1 | 23,041.27 | 7.52 | 0.0288 | |
B2 | 19,944.76 | 1 | 19,944.76 | 6.51 | 0.0380 | |
C2 | 1184.84 | 1 | 1184.84 | 0.3868 | 0.5537 | |
Residual | 21,444.47 | 7 | 3063.50 | |||
Lack of Fit | 14,433.37 | 3 | 4811.12 | 2.74 | 0.1770 | Not significant |
Pure Error | 7011.10 | 4 | 1752.77 | |||
Cor Total | 1.122 × 106 | 16 | ||||
R2 | 0.9596 | |||||
R2Adj | 0.9076 | |||||
R2pred | 0.8522 |
Accelerator | HPMC | PCE | Flowability (mm) | Dynamic Yield Stress (Pa) | Desirability |
---|---|---|---|---|---|
0.321% | 0.241% | 0.231% | 153.763 | 768.031 | 1 |
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Wang, C.; Lian, J.; Fang, Y.; Fan, G.; Yang, Y.; Huang, W.; Shi, S. Rheological Optimization of 3D-Printed Cementitious Materials Using Response Surface Methodology. Materials 2025, 18, 3933. https://doi.org/10.3390/ma18173933
Wang C, Lian J, Fang Y, Fan G, Yang Y, Huang W, Shi S. Rheological Optimization of 3D-Printed Cementitious Materials Using Response Surface Methodology. Materials. 2025; 18(17):3933. https://doi.org/10.3390/ma18173933
Chicago/Turabian StyleWang, Chenfei, Junyin Lian, Yunhui Fang, Guangming Fan, Yixin Yang, Wenkai Huang, and Shuqin Shi. 2025. "Rheological Optimization of 3D-Printed Cementitious Materials Using Response Surface Methodology" Materials 18, no. 17: 3933. https://doi.org/10.3390/ma18173933
APA StyleWang, C., Lian, J., Fang, Y., Fan, G., Yang, Y., Huang, W., & Shi, S. (2025). Rheological Optimization of 3D-Printed Cementitious Materials Using Response Surface Methodology. Materials, 18(17), 3933. https://doi.org/10.3390/ma18173933