硅酸盐通报 ›› 2026, Vol. 45 ›› Issue (2): 549-561.DOI: 10.16552/j.cnki.issn1001-1625.2025.0849
张小龙1(
), 孙为国1, 王伟1, 王朝晖2, 晏茂豪3, 刘红强1, 杨军宏1
收稿日期:2025-08-21
修订日期:2025-11-26
出版日期:2026-02-20
发布日期:2026-03-09
作者简介:张小龙(1976—),男,高级工程师。主要从事土木工程绿色低碳新材料方面的研究。E-mail:Zxl_159357@126.com
基金资助:
ZHANG Xiaolong1(
), SUN Weiguo1, WANG Wei1, WANG Zhaohui2, YAN Maohao3, LIU Hongqiang1, YANG Junhong1
Received:2025-08-21
Revised:2025-11-26
Published:2026-02-20
Online:2026-03-09
摘要:
为提高工业固废资源化利用率,本研究基于Design-Expert软件中的Mixture-Optimal(Custom)Design方法,系统研究了矿渣、钢渣及脱硫石膏三元体系对全固废胶凝材料工作性能与力学性能的协同调控作用。结果表明:三元固废体系对流动性和凝结性能具有显著调控作用,当矿渣掺量50.75%(质量分数,下同)、钢渣掺量40.00%及脱硫石膏掺量9.25%时,胶砂流动度最高可达205 mm,初凝时间及终凝时间分别缩短至170 与490 min,这主要归因于钢渣颗粒的骨架效应与脱硫石膏中
中图分类号:
张小龙, 孙为国, 王伟, 王朝晖, 晏茂豪, 刘红强, 杨军宏. 基于响应面法的全固废胶凝材料配合比优化设计及性能研究[J]. 硅酸盐通报, 2026, 45(2): 549-561.
ZHANG Xiaolong, SUN Weiguo, WANG Wei, WANG Zhaohui, YAN Maohao, LIU Hongqiang, YANG Junhong. Mix Proportion Optimization Design and Performance Study of All-Solid Waste Cementitious Materials Based on Response Surface Methodology[J]. BULLETIN OF THE CHINESE CERAMIC SOCIETY, 2026, 45(2): 549-561.
| Material | Mass fraction/% | |||||||
|---|---|---|---|---|---|---|---|---|
| CaO | SiO2 | Fe2O3 | Al2O3 | SO3 | MgO | K2O | Na2O | |
| GGBFS | 47.67 | 30.29 | 0.72 | 11.89 | 2.09 | 5.17 | 0.34 | 0.35 |
| SS | 49.32 | 45.42 | 0.44 | 0.52 | 2.27 | 0.54 | 0.12 | 0.15 |
| FGD | 44.25 | 1.43 | 14.35 | 9.00 | 20.96 | 6.40 | 0.21 | 0.46 |
表1 固废胶凝材料主要化学成分
Table 1 Main chemical composition of solid waste cementitious materials
| Material | Mass fraction/% | |||||||
|---|---|---|---|---|---|---|---|---|
| CaO | SiO2 | Fe2O3 | Al2O3 | SO3 | MgO | K2O | Na2O | |
| GGBFS | 47.67 | 30.29 | 0.72 | 11.89 | 2.09 | 5.17 | 0.34 | 0.35 |
| SS | 49.32 | 45.42 | 0.44 | 0.52 | 2.27 | 0.54 | 0.12 | 0.15 |
| FGD | 44.25 | 1.43 | 14.35 | 9.00 | 20.96 | 6.40 | 0.21 | 0.46 |
| Sample No. | Mass fraction/% | Fluidity/mm | Initial setting time/min | Final setting time/min | 28 d compressive strength/MPa | 28 d flexural strength/MPa | ||
|---|---|---|---|---|---|---|---|---|
| GGBFS | SS | FGD | ||||||
| X1 | 70.33 | 29.67 | 0 | 168 | 264 | 638 | 44.2 | 8.1 |
| X2 | 56.26 | 33.74 | 10.00 | 187 | 190 | 520 | 40.0 | 7.5 |
| X3 | 70.33 | 25.08 | 4.60 | 170 | 235 | 605 | 44.7 | 8.4 |
| X4 | 66.10 | 23.90 | 10.00 | 178 | 210 | 560 | 42.9 | 7.9 |
| X5 | 60.85 | 29.15 | 10.00 | 181 | 199 | 553 | 42.6 | 8.0 |
| X6 | 59.63 | 40.00 | 0.37 | 196 | 222 | 508 | 40.3 | 7.3 |
| X7 | 63.66 | 31.48 | 4.86 | 173 | 247 | 578 | 43.8 | 8.0 |
| X8 | 50.75 | 40.00 | 9.25 | 205 | 170 | 490 | 36.8 | 6.6 |
| X9 | 63.66 | 31.48 | 4.86 | 171 | 242 | 572 | 44.6 | 8.3 |
| X10 | 63.66 | 31.48 | 4.86 | 175 | 250 | 580 | 43.3 | 8.1 |
| X11 | 59.63 | 40.00 | 0.37 | 193 | 218 | 502 | 38.5 | 7.3 |
| X12 | 55.76 | 38.78 | 5.45 | 200 | 215 | 540 | 40.8 | 7.7 |
| X13 | 75.13 | 20.00 | 4.87 | 166 | 277 | 652 | 45.3 | 8.6 |
| X14 | 75.95 | 24.05 | 0 | 171 | 292 | 683 | 42.1 | 7.9 |
| X15 | 75.13 | 20.00 | 4.87 | 164 | 273 | 648 | 44.9 | 8.5 |
| X16 | 75.95 | 24.05 | 0 | 169 | 288 | 677 | 43.4 | 8.1 |
表2 配合比设计方案及性能测试结果
Table 2 Mix proportion design scheme and performance test results
| Sample No. | Mass fraction/% | Fluidity/mm | Initial setting time/min | Final setting time/min | 28 d compressive strength/MPa | 28 d flexural strength/MPa | ||
|---|---|---|---|---|---|---|---|---|
| GGBFS | SS | FGD | ||||||
| X1 | 70.33 | 29.67 | 0 | 168 | 264 | 638 | 44.2 | 8.1 |
| X2 | 56.26 | 33.74 | 10.00 | 187 | 190 | 520 | 40.0 | 7.5 |
| X3 | 70.33 | 25.08 | 4.60 | 170 | 235 | 605 | 44.7 | 8.4 |
| X4 | 66.10 | 23.90 | 10.00 | 178 | 210 | 560 | 42.9 | 7.9 |
| X5 | 60.85 | 29.15 | 10.00 | 181 | 199 | 553 | 42.6 | 8.0 |
| X6 | 59.63 | 40.00 | 0.37 | 196 | 222 | 508 | 40.3 | 7.3 |
| X7 | 63.66 | 31.48 | 4.86 | 173 | 247 | 578 | 43.8 | 8.0 |
| X8 | 50.75 | 40.00 | 9.25 | 205 | 170 | 490 | 36.8 | 6.6 |
| X9 | 63.66 | 31.48 | 4.86 | 171 | 242 | 572 | 44.6 | 8.3 |
| X10 | 63.66 | 31.48 | 4.86 | 175 | 250 | 580 | 43.3 | 8.1 |
| X11 | 59.63 | 40.00 | 0.37 | 193 | 218 | 502 | 38.5 | 7.3 |
| X12 | 55.76 | 38.78 | 5.45 | 200 | 215 | 540 | 40.8 | 7.7 |
| X13 | 75.13 | 20.00 | 4.87 | 166 | 277 | 652 | 45.3 | 8.6 |
| X14 | 75.95 | 24.05 | 0 | 171 | 292 | 683 | 42.1 | 7.9 |
| X15 | 75.13 | 20.00 | 4.87 | 164 | 273 | 648 | 44.9 | 8.5 |
| X16 | 75.95 | 24.05 | 0 | 169 | 288 | 677 | 43.4 | 8.1 |
| Source | Sum of square | df | Mean square | F-value | P-value | Significance |
|---|---|---|---|---|---|---|
| Model | 85.47 | 5 | 17.09 | 28.46 | <0.000 1 | Significance |
| Linear mixture | 59.62 | 2 | 29.81 | 49.64 | <0.000 1 | — |
| AB | 11.93 | 1 | 11.93 | 19.86 | 0.001 2 | — |
| AC | 13.94 | 1 | 13.94 | 23.22 | 0.000 7 | — |
| BC | 10.30 | 1 | 10.30 | 17.15 | 0.002 0 | — |
| Residual | 6.01 | 10 | 0.600 6 | — | — | — |
| Lack of fit | 2.60 | 5 | 0.520 1 | 0.763 8 | 0.612 7 | Not significance |
| Pure error | 3.40 | 5 | 0.681 0 | — | — | — |
表3 28 d抗压强度回归模型方差分析
Table 3 Variance analysis of regression model for 28 d compressive strength
| Source | Sum of square | df | Mean square | F-value | P-value | Significance |
|---|---|---|---|---|---|---|
| Model | 85.47 | 5 | 17.09 | 28.46 | <0.000 1 | Significance |
| Linear mixture | 59.62 | 2 | 29.81 | 49.64 | <0.000 1 | — |
| AB | 11.93 | 1 | 11.93 | 19.86 | 0.001 2 | — |
| AC | 13.94 | 1 | 13.94 | 23.22 | 0.000 7 | — |
| BC | 10.30 | 1 | 10.30 | 17.15 | 0.002 0 | — |
| Residual | 6.01 | 10 | 0.600 6 | — | — | — |
| Lack of fit | 2.60 | 5 | 0.520 1 | 0.763 8 | 0.612 7 | Not significance |
| Pure error | 3.40 | 5 | 0.681 0 | — | — | — |
| Evaluation index | Complex correlation coefficient (R2) | Correction correlation coefficient(Adjusted R2) | Predictive correlation coefficient(Predicted R2) | Coefficient of variation(C.V.)/% | Signal noise ratio |
|---|---|---|---|---|---|
| Correlation coefficient | 0.934 3 | 0.901 5 | 0.827 8 | 1.83 | 17.549 4 |
表4 回归模型相关性评估
Table 4 Correlation assessment of regression model
| Evaluation index | Complex correlation coefficient (R2) | Correction correlation coefficient(Adjusted R2) | Predictive correlation coefficient(Predicted R2) | Coefficient of variation(C.V.)/% | Signal noise ratio |
|---|---|---|---|---|---|
| Correlation coefficient | 0.934 3 | 0.901 5 | 0.827 8 | 1.83 | 17.549 4 |
| Source | Sum of square | df | Mean square | F-value | P-value | Significance |
|---|---|---|---|---|---|---|
| Model | 3.76 | 5 | 0.752 9 | 25.95 | <0.000 1 | Significance |
| Linear mixture | 2.79 | 2 | 1.40 | 48.10 | <0.000 1 | — |
| AB | 0.297 7 | 1 | 0.297 7 | 10.26 | 0.009 4 | — |
| AC | 0.635 4 | 1 | 0.635 4 | 21.91 | 0.000 9 | — |
| BC | 0.411 7 | 1 | 0.411 7 | 14.19 | 0.003 7 | — |
| Residual | 0.290 1 | 10 | 0.029 0 | — | — | — |
| Lack of fit | 0.217 2 | 5 | 0.043 4 | 2.98 | 0.128 1 | Not significance |
| Pure error | 0.072 9 | 5 | 0.014 6 | — | — | — |
表5 28 d抗折强度回归模型方差分析
Table 5 Variance analysis of regression model for 28 d flexural strength
| Source | Sum of square | df | Mean square | F-value | P-value | Significance |
|---|---|---|---|---|---|---|
| Model | 3.76 | 5 | 0.752 9 | 25.95 | <0.000 1 | Significance |
| Linear mixture | 2.79 | 2 | 1.40 | 48.10 | <0.000 1 | — |
| AB | 0.297 7 | 1 | 0.297 7 | 10.26 | 0.009 4 | — |
| AC | 0.635 4 | 1 | 0.635 4 | 21.91 | 0.000 9 | — |
| BC | 0.411 7 | 1 | 0.411 7 | 14.19 | 0.003 7 | — |
| Residual | 0.290 1 | 10 | 0.029 0 | — | — | — |
| Lack of fit | 0.217 2 | 5 | 0.043 4 | 2.98 | 0.128 1 | Not significance |
| Pure error | 0.072 9 | 5 | 0.014 6 | — | — | — |
| Evaluation index | Complex correlation coefficient (R2) | Correction correlation coefficient(Adjusted R2) | Predictive correlation coefficient(Predicted R2) | Coefficient of variation(C.V.)/% | Signal noise ratio |
|---|---|---|---|---|---|
| Correlation coefficient | 0.928 5 | 0.892 7 | 0.752 0 | 2.16 | 16.527 8 |
表6 回归模型相关性评估
Table 6 Correlation assessment of regression model
| Evaluation index | Complex correlation coefficient (R2) | Correction correlation coefficient(Adjusted R2) | Predictive correlation coefficient(Predicted R2) | Coefficient of variation(C.V.)/% | Signal noise ratio |
|---|---|---|---|---|---|
| Correlation coefficient | 0.928 5 | 0.892 7 | 0.752 0 | 2.16 | 16.527 8 |
| Project | Factor | Response indicator | ||||||
|---|---|---|---|---|---|---|---|---|
| Indicator | Mass fraction/% | Fluidity/mm | Initial settingtime/min | Final settingtime/min | 28 d compressivestrength/MPa | 28 d flexuralstrength/MPa | ||
| GGBFS | SS | FGD | ||||||
| Lower limit | 50 | 20 | 0 | 164 | 170 | 490 | 36.8 | 6.6 |
| Upper limit | 80 | 40 | 10 | 205 | 292 | 683 | 45.3 | 8.6 |
| Objective | — | — | — | ≥180 | ≥240 | ≤600 | ≥42.5 | ≥7.0 |
表7 影响因素取值范围与预测值
Table 7 Range of influencing factors and predicted value
| Project | Factor | Response indicator | ||||||
|---|---|---|---|---|---|---|---|---|
| Indicator | Mass fraction/% | Fluidity/mm | Initial settingtime/min | Final settingtime/min | 28 d compressivestrength/MPa | 28 d flexuralstrength/MPa | ||
| GGBFS | SS | FGD | ||||||
| Lower limit | 50 | 20 | 0 | 164 | 170 | 490 | 36.8 | 6.6 |
| Upper limit | 80 | 40 | 10 | 205 | 292 | 683 | 45.3 | 8.6 |
| Objective | — | — | — | ≥180 | ≥240 | ≤600 | ≥42.5 | ≥7.0 |
| Mass fraction/% | Measured value | Predicted value | Relative error/% | |||
|---|---|---|---|---|---|---|
| GGBFS | SS | FGD | ||||
| 63.6 | 34.9 | 1.5 | Fluidity/mm | 185 | 180 | 2.78 |
| Initial setting time/min | 240 | 243 | 1.23 | |||
| Final setting time/min | 572 | 566 | 1.06 | |||
| 28 d compressive strength/MPa | 44.3 | 42.5 | 3.75 | |||
| 28 d flexural strength/MPa | 7.96 | 7.87 | 1.14 | |||
表8 最优配合比下各响应指标实测值与预测值对比
Table 8 Comparison of measured value and predicted value for each response indicator at optimal mix proportion
| Mass fraction/% | Measured value | Predicted value | Relative error/% | |||
|---|---|---|---|---|---|---|
| GGBFS | SS | FGD | ||||
| 63.6 | 34.9 | 1.5 | Fluidity/mm | 185 | 180 | 2.78 |
| Initial setting time/min | 240 | 243 | 1.23 | |||
| Final setting time/min | 572 | 566 | 1.06 | |||
| 28 d compressive strength/MPa | 44.3 | 42.5 | 3.75 | |||
| 28 d flexural strength/MPa | 7.96 | 7.87 | 1.14 | |||
| Material | Content/kg | Carbon emission factor/(kg CO2-eq·kg-1) | Carbon emission/kg CO2-eq | Unit price/(yuan·t-1) |
|---|---|---|---|---|
| GGBFS | 636 | 0.004 7[ | 2.99 | 380[ |
| SS | 349 | 0.34[ | 118.66 | 120 |
| FGD | 15 | — | — | — |
| OPC | 1 000 | 0.87[ | 870 | 600[ |
表9 全固废胶凝材料碳排放与经济成本分析
Table 9 Carbon emission and economic cost analysis of all-solid waste cementitious materials
| Material | Content/kg | Carbon emission factor/(kg CO2-eq·kg-1) | Carbon emission/kg CO2-eq | Unit price/(yuan·t-1) |
|---|---|---|---|---|
| GGBFS | 636 | 0.004 7[ | 2.99 | 380[ |
| SS | 349 | 0.34[ | 118.66 | 120 |
| FGD | 15 | — | — | — |
| OPC | 1 000 | 0.87[ | 870 | 600[ |
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