硅酸盐通报 ›› 2026, Vol. 45 ›› Issue (2): 695-711.DOI: 10.16552/j.cnki.issn1001-1625.2025.0812
刘梅芳1(
), 刘建正2, 胡力群1(
), 高胜发2, 刘家宏2, 李国超2
收稿日期:2025-08-11
修订日期:2025-09-29
出版日期:2026-02-20
发布日期:2026-03-09
通信作者:
胡力群,博士,教授。E-mail:hlq123@126.com作者简介:刘梅芳(2001—),女,硕士研究生。主要从事道路材料的研究。E-mail:l15526009021@163.com
基金资助:
LIU Meifang1(
), LIU Jianzheng2, HU Liqun1(
), GAO Shengfa2, LIU Jiahong2, LI Guochao2
Received:2025-08-11
Revised:2025-09-29
Published:2026-02-20
Online:2026-03-09
摘要:
为了给地聚物注浆材料在道路非开挖注浆加固等工程中的推广应用提供配合比设计参考与理论支撑,针对矿渣-粉煤灰地聚物注浆材料(SFGGM),采用四因素四水平正交试验,通过极差与方差分析得到了水胶比、碱当量、水玻璃模数及粉煤灰掺量对流动度、凝结时间、干缩率及力学性能等多项关键指标的影响。在此基础上,结合AHP-熵值法进行多指标综合权重分析,选出兼顾工作性能、体积稳定性及力学性能的最优配合比方案。结果表明:水胶比对流动度的影响最显著,随着水胶比增加,浆体流动性明显提升;碱当量是控制凝结时间与干缩率的主导因素,碱当量过高会导致凝结时间缩短和干缩率增加;粉煤灰掺量是影响抗压强度与抗折强度的关键因素,掺量过高导致抗压强度与抗折强度下降;适度提高碱当量和水玻璃模数有助于促进强度发展。极差分析与方差分析得出的各性能指标的主影响因素一致,综合性能最优的配合比为水胶比0.6、水玻璃模数1.6、碱当量6%(质量分数)、粉煤灰掺量0.4(占硅铝源灰料总质量的比例)。
中图分类号:
刘梅芳, 刘建正, 胡力群, 高胜发, 刘家宏, 李国超. 矿渣-粉煤灰地聚物注浆材料配合比优化研究[J]. 硅酸盐通报, 2026, 45(2): 695-711.
LIU Meifang, LIU Jianzheng, HU Liqun, GAO Shengfa, LIU Jiahong, LI Guochao. Mix Ratio Optimization of Slag-Fly Ash Geopolymer Grouting Materials[J]. BULLETIN OF THE CHINESE CERAMIC SOCIETY, 2026, 45(2): 695-711.
| Material | Mass fraction/% | |||||
|---|---|---|---|---|---|---|
| SiO2 | Al2O3 | CaO | MgO | Fe2O3 | SO3 | |
| Slag | 34.50 | 17.70 | 34.00 | 6.01 | 1.03 | 1.64 |
| Fly ash | 43.00 | 23.00 | 5.60 | 0.95 | 2.50 | 0.80 |
表1 矿渣和粉煤灰的主要化学成分
Table 1 Main chemical composition of slag and fly ash
| Material | Mass fraction/% | |||||
|---|---|---|---|---|---|---|
| SiO2 | Al2O3 | CaO | MgO | Fe2O3 | SO3 | |
| Slag | 34.50 | 17.70 | 34.00 | 6.01 | 1.03 | 1.64 |
| Fly ash | 43.00 | 23.00 | 5.60 | 0.95 | 2.50 | 0.80 |
| Performance indicator | Density/(g·cm-3) | Fineness/% | Waterdemandratio/% | Loss on ignition/% | Moisture content/% | Specific surface area/(m2·kg-1) | Flow ratio/% | 7 d activity index/% | 28 d activity index/% |
|---|---|---|---|---|---|---|---|---|---|
| Slag | 3.10 | 0.84 | 0.45 | 429.00 | 98.00 | 84.20 | 98.50 | ||
| Fly ash | 2.55 | 13.00 | 91.00 | 3.01 | 0.85 |
表2 矿渣和粉煤灰的物理性能指标
Table 2 Physical property index of slag and fly ash
| Performance indicator | Density/(g·cm-3) | Fineness/% | Waterdemandratio/% | Loss on ignition/% | Moisture content/% | Specific surface area/(m2·kg-1) | Flow ratio/% | 7 d activity index/% | 28 d activity index/% |
|---|---|---|---|---|---|---|---|---|---|
| Slag | 3.10 | 0.84 | 0.45 | 429.00 | 98.00 | 84.20 | 98.50 | ||
| Fly ash | 2.55 | 13.00 | 91.00 | 3.01 | 0.85 |
| Level | A | B | C/% | D |
|---|---|---|---|---|
| 1 | 0.3 | 1.4 | 2 | 0.4 |
| 2 | 0.4 | 1.6 | 4 | 0.5 |
| 3 | 0.5 | 1.8 | 6 | 0.6 |
| 4 | 0.6 | 2.0 | 8 | 0.7 |
表3 正交试验因素水平表
Table 3 Factor and level table of orthogonal experiment
| Level | A | B | C/% | D |
|---|---|---|---|---|
| 1 | 0.3 | 1.4 | 2 | 0.4 |
| 2 | 0.4 | 1.6 | 4 | 0.5 |
| 3 | 0.5 | 1.8 | 6 | 0.6 |
| 4 | 0.6 | 2.0 | 8 | 0.7 |
| Test number | A | B | C/% | D |
|---|---|---|---|---|
| 1 | 0.3 | 1.4 | 2 | 0.4 |
| 2 | 0.3 | 1.6 | 4 | 0.5 |
| 3 | 0.3 | 1.8 | 6 | 0.6 |
| 4 | 0.3 | 2.0 | 8 | 0.7 |
| 5 | 0.4 | 1.4 | 4 | 0.6 |
| 6 | 0.4 | 1.6 | 2 | 0.7 |
| 7 | 0.4 | 1.8 | 8 | 0.4 |
| 8 | 0.4 | 2.0 | 6 | 0.5 |
| 9 | 0.5 | 1.4 | 6 | 0.7 |
| 10 | 0.5 | 1.6 | 8 | 0.6 |
| 11 | 0.5 | 1.8 | 2 | 0.5 |
| 12 | 0.5 | 2.0 | 4 | 0.4 |
| 13 | 0.6 | 1.4 | 8 | 0.5 |
| 14 | 0.6 | 1.6 | 6 | 0.4 |
| 15 | 0.6 | 1.8 | 4 | 0.7 |
| 16 | 0.6 | 2.0 | 2 | 0.6 |
表4 正交试验方案
Table 4 Orthogonal test scheme
| Test number | A | B | C/% | D |
|---|---|---|---|---|
| 1 | 0.3 | 1.4 | 2 | 0.4 |
| 2 | 0.3 | 1.6 | 4 | 0.5 |
| 3 | 0.3 | 1.8 | 6 | 0.6 |
| 4 | 0.3 | 2.0 | 8 | 0.7 |
| 5 | 0.4 | 1.4 | 4 | 0.6 |
| 6 | 0.4 | 1.6 | 2 | 0.7 |
| 7 | 0.4 | 1.8 | 8 | 0.4 |
| 8 | 0.4 | 2.0 | 6 | 0.5 |
| 9 | 0.5 | 1.4 | 6 | 0.7 |
| 10 | 0.5 | 1.6 | 8 | 0.6 |
| 11 | 0.5 | 1.8 | 2 | 0.5 |
| 12 | 0.5 | 2.0 | 4 | 0.4 |
| 13 | 0.6 | 1.4 | 8 | 0.5 |
| 14 | 0.6 | 1.6 | 6 | 0.4 |
| 15 | 0.6 | 1.8 | 4 | 0.7 |
| 16 | 0.6 | 2.0 | 2 | 0.6 |
| Testnumber | Fluidity/mm | Setting time/min | Drying shrinkage rate/% | Compressive strength/MPa | Flexural strength/MPa | ||||
|---|---|---|---|---|---|---|---|---|---|
| Initial | Final | 7 d | 28 d | 7 d | 28 d | 7 d | 28 d | ||
| 1 | 60 | 72 | 158 | 0.199 | 0.251 | 28.7 | 44.8 | 5.7 | 6.6 |
| 2 | 117 | 10 | 15 | 0.316 | 0.348 | 69.1 | 82.8 | 4.8 | 5.5 |
| 3 | 175 | 17 | 21 | 0.458 | 0.580 | 46.6 | 71.8 | 2.6 | 2.7 |
| 4 | 177 | 34 | 39 | 0.992 | 1.650 | 27.2 | 41.8 | 1.9 | 3.3 |
| 5 | 154 | 21 | 30 | 0.051 | 0.107 | 0.9 | 1.7 | 0.3 | 0.5 |
| 6 | 118 | 784 | 1 149 | 0.034 | 0.039 | 0.1 | 0.2 | 0.1 | 0.1 |
| 7 | 234 | 13 | 16 | 0.602 | 0.614 | 59.0 | 63.1 | 3.3 | 3.8 |
| 8 | 226 | 14 | 17 | 0.762 | 0.915 | 49.7 | 56.5 | 2.9 | 3.4 |
| 9 | 247 | 37 | 66 | 0.394 | 0.448 | 0.7 | 1.3 | 0.4 | 0.5 |
| 10 | 278 | 19 | 27 | 0.846 | 1.530 | 28.5 | 46.4 | 4.3 | 4.9 |
| 11 | 191 | 375 | 505 | 0.168 | 0.242 | 12.7 | 16.7 | 4.2 | 5.4 |
| 12 | 233 | 100 | 106 | 1.291 | 1.424 | 43.5 | 47.1 | 2.7 | 3.2 |
| 13 | 278 | 47 | 69 | 1.345 | 1.771 | 32.9 | 46.0 | 0.4 | 0.6 |
| 14 | 282 | 53 | 107 | 0.817 | 1.270 | 34.0 | 40.6 | 6.8 | 7.5 |
| 15 | 253 | 132 | 176 | 0.145 | 0.196 | 0.1 | 0.1 | 0 | 0.1 |
| 16 | 223 | 1 380 | 2 100 | 0.114 | 0.271 | 0.1 | 0.2 | 0.1 | 0.1 |
表5 正交试验结果
Table 5 Results of orthogonal test
| Testnumber | Fluidity/mm | Setting time/min | Drying shrinkage rate/% | Compressive strength/MPa | Flexural strength/MPa | ||||
|---|---|---|---|---|---|---|---|---|---|
| Initial | Final | 7 d | 28 d | 7 d | 28 d | 7 d | 28 d | ||
| 1 | 60 | 72 | 158 | 0.199 | 0.251 | 28.7 | 44.8 | 5.7 | 6.6 |
| 2 | 117 | 10 | 15 | 0.316 | 0.348 | 69.1 | 82.8 | 4.8 | 5.5 |
| 3 | 175 | 17 | 21 | 0.458 | 0.580 | 46.6 | 71.8 | 2.6 | 2.7 |
| 4 | 177 | 34 | 39 | 0.992 | 1.650 | 27.2 | 41.8 | 1.9 | 3.3 |
| 5 | 154 | 21 | 30 | 0.051 | 0.107 | 0.9 | 1.7 | 0.3 | 0.5 |
| 6 | 118 | 784 | 1 149 | 0.034 | 0.039 | 0.1 | 0.2 | 0.1 | 0.1 |
| 7 | 234 | 13 | 16 | 0.602 | 0.614 | 59.0 | 63.1 | 3.3 | 3.8 |
| 8 | 226 | 14 | 17 | 0.762 | 0.915 | 49.7 | 56.5 | 2.9 | 3.4 |
| 9 | 247 | 37 | 66 | 0.394 | 0.448 | 0.7 | 1.3 | 0.4 | 0.5 |
| 10 | 278 | 19 | 27 | 0.846 | 1.530 | 28.5 | 46.4 | 4.3 | 4.9 |
| 11 | 191 | 375 | 505 | 0.168 | 0.242 | 12.7 | 16.7 | 4.2 | 5.4 |
| 12 | 233 | 100 | 106 | 1.291 | 1.424 | 43.5 | 47.1 | 2.7 | 3.2 |
| 13 | 278 | 47 | 69 | 1.345 | 1.771 | 32.9 | 46.0 | 0.4 | 0.6 |
| 14 | 282 | 53 | 107 | 0.817 | 1.270 | 34.0 | 40.6 | 6.8 | 7.5 |
| 15 | 253 | 132 | 176 | 0.145 | 0.196 | 0.1 | 0.1 | 0 | 0.1 |
| 16 | 223 | 1 380 | 2 100 | 0.114 | 0.271 | 0.1 | 0.2 | 0.1 | 0.1 |
| Indicator | Range | A | B | C | D |
|---|---|---|---|---|---|
| Fluidity | k1 | 132.25 | 184.75 | 148.00 | 202.25 |
| k2 | 183.00 | 198.75 | 189.25 | 203.00 | |
| k3 | 237.25 | 213.25 | 232.50 | 207.50 | |
| k4 | 259.00 | 214.75 | 241.75 | 198.75 | |
| R | 126.75 | 30.00 | 93.75 | 8.75 | |
| Initial setting time | k1 | 33.25 | 44.25 | 652.75 | 59.50 |
| k2 | 208.00 | 216.50 | 65.75 | 111.50 | |
| k3 | 132.75 | 134.25 | 30.25 | 359.25 | |
| k4 | 403.00 | 382.00 | 28.25 | 246.75 | |
| R | 369.75 | 337.75 | 624.50 | 299.75 | |
| Final setting time | k1 | 58.25 | 80.75 | 978.00 | 96.75 |
| k2 | 303.00 | 324.50 | 81.75 | 151.50 | |
| k3 | 176.00 | 179.50 | 52.75 | 544.50 | |
| k4 | 613.00 | 565.50 | 37.75 | 357.50 | |
| R | 554.75 | 484.75 | 940.25 | 447.75 |
表6 工作性能的极差分析
Table 6 Range analysis of workability
| Indicator | Range | A | B | C | D |
|---|---|---|---|---|---|
| Fluidity | k1 | 132.25 | 184.75 | 148.00 | 202.25 |
| k2 | 183.00 | 198.75 | 189.25 | 203.00 | |
| k3 | 237.25 | 213.25 | 232.50 | 207.50 | |
| k4 | 259.00 | 214.75 | 241.75 | 198.75 | |
| R | 126.75 | 30.00 | 93.75 | 8.75 | |
| Initial setting time | k1 | 33.25 | 44.25 | 652.75 | 59.50 |
| k2 | 208.00 | 216.50 | 65.75 | 111.50 | |
| k3 | 132.75 | 134.25 | 30.25 | 359.25 | |
| k4 | 403.00 | 382.00 | 28.25 | 246.75 | |
| R | 369.75 | 337.75 | 624.50 | 299.75 | |
| Final setting time | k1 | 58.25 | 80.75 | 978.00 | 96.75 |
| k2 | 303.00 | 324.50 | 81.75 | 151.50 | |
| k3 | 176.00 | 179.50 | 52.75 | 544.50 | |
| k4 | 613.00 | 565.50 | 37.75 | 357.50 | |
| R | 554.75 | 484.75 | 940.25 | 447.75 |
| Indicator | Range | A | B | C | D |
|---|---|---|---|---|---|
| 7 d drying shrinkage rate | k1 | 0.491 3 | 0.497 2 | 0.128 8 | 0.727 2 |
| k2 | 0.362 2 | 0.503 2 | 0.450 7 | 0.647 8 | |
| k3 | 0.674 7 | 0.343 2 | 0.607 8 | 0.367 3 | |
| k4 | 0.605 2 | 0.789 7 | 0.946 3 | 0.391 2 | |
| R | 0.312 5 | 0.446 5 | 0.817 5 | 0.360 0 | |
| 28 d drying shrinkage rate | k1 | 0.707 2 | 0.644 2 | 0.200 8 | 0.889 7 |
| k2 | 0.418 8 | 0.796 8 | 0.518 8 | 0.819 0 | |
| k3 | 0.911 0 | 0.408 0 | 0.803 3 | 0.622 0 | |
| k4 | 0.887 0 | 1.065 0 | 1.391 2 | 0.583 3 | |
| R | 0.492 2 | 0.657 0 | 1.190 5 | 0.306 5 |
表7 干缩率的极差分析
Table 7 Range analysis of drying shrinkage rate
| Indicator | Range | A | B | C | D |
|---|---|---|---|---|---|
| 7 d drying shrinkage rate | k1 | 0.491 3 | 0.497 2 | 0.128 8 | 0.727 2 |
| k2 | 0.362 2 | 0.503 2 | 0.450 7 | 0.647 8 | |
| k3 | 0.674 7 | 0.343 2 | 0.607 8 | 0.367 3 | |
| k4 | 0.605 2 | 0.789 7 | 0.946 3 | 0.391 2 | |
| R | 0.312 5 | 0.446 5 | 0.817 5 | 0.360 0 | |
| 28 d drying shrinkage rate | k1 | 0.707 2 | 0.644 2 | 0.200 8 | 0.889 7 |
| k2 | 0.418 8 | 0.796 8 | 0.518 8 | 0.819 0 | |
| k3 | 0.911 0 | 0.408 0 | 0.803 3 | 0.622 0 | |
| k4 | 0.887 0 | 1.065 0 | 1.391 2 | 0.583 3 | |
| R | 0.492 2 | 0.657 0 | 1.190 5 | 0.306 5 |
| Indicator | Range | A | B | C | D |
|---|---|---|---|---|---|
| 7 d compressive strength | k1 | 42.900 | 15.800 | 10.400 | 41.300 |
| k2 | 27.425 | 32.925 | 28.400 | 41.100 | |
| k3 | 21.350 | 29.600 | 32.750 | 19.025 | |
| k4 | 16.775 | 30.125 | 36.900 | 7.025 | |
| R | 26.125 | 17.125 | 26.500 | 34.275 | |
| 28 d compressive strength | k1 | 60.300 | 23.450 | 15.480 | 48.900 |
| k2 | 30.380 | 42.500 | 32.920 | 50.500 | |
| k3 | 27.880 | 37.920 | 42.550 | 30.030 | |
| k4 | 21.720 | 36.400 | 49.330 | 10.850 | |
| R | 38.580 | 19.050 | 33.850 | 39.650 | |
| 7 d flexural strength | k1 | 3.750 | 1.700 | 2.525 | 4.625 |
| k2 | 1.650 | 4.000 | 1.950 | 3.075 | |
| k3 | 2.900 | 2.525 | 3.175 | 1.825 | |
| k4 | 1.825 | 1.900 | 2.475 | 0.600 | |
| R | 2.100 | 2.300 | 1.225 | 4.025 | |
| 28 d flexural strength | k1 | 4.525 | 2.050 | 3.050 | 5.275 |
| k2 | 1.950 | 4.500 | 2.325 | 3.725 | |
| k3 | 3.500 | 3.000 | 3.525 | 2.050 | |
| k4 | 2.075 | 2.500 | 3.150 | 1.000 | |
| R | 2.575 | 2.450 | 1.200 | 4.275 |
表8 力学性能的极差分析
Table 8 Range analysis of mechanical properties
| Indicator | Range | A | B | C | D |
|---|---|---|---|---|---|
| 7 d compressive strength | k1 | 42.900 | 15.800 | 10.400 | 41.300 |
| k2 | 27.425 | 32.925 | 28.400 | 41.100 | |
| k3 | 21.350 | 29.600 | 32.750 | 19.025 | |
| k4 | 16.775 | 30.125 | 36.900 | 7.025 | |
| R | 26.125 | 17.125 | 26.500 | 34.275 | |
| 28 d compressive strength | k1 | 60.300 | 23.450 | 15.480 | 48.900 |
| k2 | 30.380 | 42.500 | 32.920 | 50.500 | |
| k3 | 27.880 | 37.920 | 42.550 | 30.030 | |
| k4 | 21.720 | 36.400 | 49.330 | 10.850 | |
| R | 38.580 | 19.050 | 33.850 | 39.650 | |
| 7 d flexural strength | k1 | 3.750 | 1.700 | 2.525 | 4.625 |
| k2 | 1.650 | 4.000 | 1.950 | 3.075 | |
| k3 | 2.900 | 2.525 | 3.175 | 1.825 | |
| k4 | 1.825 | 1.900 | 2.475 | 0.600 | |
| R | 2.100 | 2.300 | 1.225 | 4.025 | |
| 28 d flexural strength | k1 | 4.525 | 2.050 | 3.050 | 5.275 |
| k2 | 1.950 | 4.500 | 2.325 | 3.725 | |
| k3 | 3.500 | 3.000 | 3.525 | 2.050 | |
| k4 | 2.075 | 2.500 | 3.150 | 1.000 | |
| R | 2.575 | 2.450 | 1.200 | 4.275 |
| Performance index | Factor | Adj SS | df | Adj MS | F | p | Factor order |
|---|---|---|---|---|---|---|---|
| Fluidity | A | 77 756.344 | 3 | 25 918.781 | 1 268.095 | 0** | ACBD |
| B | 4 732.844 | 3 | 1 577.615 | 77.186 | 0** | ||
| C | 44 608.844 | 3 | 14 869.615 | 727.507 | 0** | ||
| D | 311.844 | 3 | 103.948 | 5.086 | 0.009** | ||
| Residual | 388.344 | 19 | 20.439 | ||||
| R2=0.997 | |||||||
| Initial setting time | A | 586 984.344 | 3 | 195 661.448 | 8.647 | 0.001** | CABD |
| B | 495 061.094 | 3 | 165 020.365 | 7.293 | 0.002** | ||
| C | 2 248 500.344 | 3 | 749 500.115 | 33.122 | 0** | ||
| D | 440 656.344 | 3 | 146 885.448 | 6.491 | 0.003** | ||
| Residual | 429 939.094 | 19 | 22 628.373 | ||||
| R2=0.898 | |||||||
| Final setting time | A | 1 361 788.844 | 3 | 453 929.615 | 8.744 | 0.001** | CABD |
| B | 1 066 407.344 | 3 | 355 469.115 | 6.847 | 0.003** | ||
| C | 5 097 442.094 | 3 | 1 699 147.365 | 32.729 | 0 ** | ||
| D | 1 005 117.094 | 3 | 335 039.031 | 6.453 | 0.003** | ||
| Residual | 986 403.844 | 19 | 51 915.992 | ||||
| R2=0.896 | |||||||
| 7 d drying shrinkage rate | A | 0.594 | 3 | 0.198 | 5.469 | 0.004** | CDBA |
| B | 1.056 | 3 | 0.352 | 9.719 | 0** | ||
| C | 3.857 | 3 | 1.286 | 35.483 | 0** | ||
| D | 1.103 | 3 | 0.368 | 10.149 | 0** | ||
| Residual | 1.015 | 28 | 0.036 | ||||
| R2=0.866 | |||||||
| 28 d drying shrinkage rate | A | 1.654 | 3 | 0.551 | 9.310 | 0** | CBAD |
| B | 2.641 | 3 | 0.880 | 14.860 | 0** | ||
| C | 7.953 | 3 | 2.651 | 44.754 | 0** | ||
| D | 0.762 | 3 | 0.254 | 4.290 | 0.013* | ||
| Residual | 1.718 | 29 | 0.059 | ||||
| R2=0.876 | |||||||
| 7 d compressive strength | A | 8 152.867 | 3 | 2 717.622 | 68.158 | 0** | DACB |
| B | 3 466.347 | 3 | 1 155.449 | 28.979 | 0** | ||
| C | 8 631.123 | 3 | 2 877.041 | 72.156 | 0** | ||
| D | 17 439.058 | 3 | 5 813.019 | 145.791 | 0** | ||
| Residual | 2 791.064 | 70 | 39.872 | ||||
| R2=0.931 | |||||||
| 28 d compressive strength | A | 19 175.184 | 3 | 6 391.728 | 134.577 | 0** | DACB |
| B | 4 787.213 | 3 | 1 595.738 | 33.598 | 0** | ||
| C | 13 474.354 | 3 | 4 491.451 | 94.567 | 0** | ||
| D | 22 480.702 | 3 | 7 493.567 | 157.776 | 0** | ||
| Residual | 3 467.127 | 73 | 47.495 | ||||
| R2=0.947 | |||||||
| 7 d flexural strength | A | 25.727 | 3 | 8.576 | 9.715 | 0** | DAB |
| B | 22.451 | 3 | 7.484 | 8.477 | 0.001** | ||
| C | 3.393 | 3 | 1.131 | 1.281 | 0.309 | ||
| D | 73.717 | 3 | 24.572 | 27.835 | 0** | ||
| Residual | 16.773 | 19 | 0.883 | ||||
| R2=0.889 | |||||||
| 28 d flexural strength | A | 27.500 | 3 | 9.167 | 5.329 | 0.008** | DAB |
| B | 24.330 | 3 | 8.110 | 4.715 | 0.013* | ||
| C | 6.366 | 3 | 2.122 | 1.234 | 0.327 | ||
| D | 93.148 | 3 | 31.049 | 18.050 | 0** | ||
| Residual | 30.963 | 18 | 1.720 | ||||
| R2=0.842 | |||||||
表9 各性能指标多因素方差分析结果
Table 9 Multi-factor ANOVA results for each performance index
| Performance index | Factor | Adj SS | df | Adj MS | F | p | Factor order |
|---|---|---|---|---|---|---|---|
| Fluidity | A | 77 756.344 | 3 | 25 918.781 | 1 268.095 | 0** | ACBD |
| B | 4 732.844 | 3 | 1 577.615 | 77.186 | 0** | ||
| C | 44 608.844 | 3 | 14 869.615 | 727.507 | 0** | ||
| D | 311.844 | 3 | 103.948 | 5.086 | 0.009** | ||
| Residual | 388.344 | 19 | 20.439 | ||||
| R2=0.997 | |||||||
| Initial setting time | A | 586 984.344 | 3 | 195 661.448 | 8.647 | 0.001** | CABD |
| B | 495 061.094 | 3 | 165 020.365 | 7.293 | 0.002** | ||
| C | 2 248 500.344 | 3 | 749 500.115 | 33.122 | 0** | ||
| D | 440 656.344 | 3 | 146 885.448 | 6.491 | 0.003** | ||
| Residual | 429 939.094 | 19 | 22 628.373 | ||||
| R2=0.898 | |||||||
| Final setting time | A | 1 361 788.844 | 3 | 453 929.615 | 8.744 | 0.001** | CABD |
| B | 1 066 407.344 | 3 | 355 469.115 | 6.847 | 0.003** | ||
| C | 5 097 442.094 | 3 | 1 699 147.365 | 32.729 | 0 ** | ||
| D | 1 005 117.094 | 3 | 335 039.031 | 6.453 | 0.003** | ||
| Residual | 986 403.844 | 19 | 51 915.992 | ||||
| R2=0.896 | |||||||
| 7 d drying shrinkage rate | A | 0.594 | 3 | 0.198 | 5.469 | 0.004** | CDBA |
| B | 1.056 | 3 | 0.352 | 9.719 | 0** | ||
| C | 3.857 | 3 | 1.286 | 35.483 | 0** | ||
| D | 1.103 | 3 | 0.368 | 10.149 | 0** | ||
| Residual | 1.015 | 28 | 0.036 | ||||
| R2=0.866 | |||||||
| 28 d drying shrinkage rate | A | 1.654 | 3 | 0.551 | 9.310 | 0** | CBAD |
| B | 2.641 | 3 | 0.880 | 14.860 | 0** | ||
| C | 7.953 | 3 | 2.651 | 44.754 | 0** | ||
| D | 0.762 | 3 | 0.254 | 4.290 | 0.013* | ||
| Residual | 1.718 | 29 | 0.059 | ||||
| R2=0.876 | |||||||
| 7 d compressive strength | A | 8 152.867 | 3 | 2 717.622 | 68.158 | 0** | DACB |
| B | 3 466.347 | 3 | 1 155.449 | 28.979 | 0** | ||
| C | 8 631.123 | 3 | 2 877.041 | 72.156 | 0** | ||
| D | 17 439.058 | 3 | 5 813.019 | 145.791 | 0** | ||
| Residual | 2 791.064 | 70 | 39.872 | ||||
| R2=0.931 | |||||||
| 28 d compressive strength | A | 19 175.184 | 3 | 6 391.728 | 134.577 | 0** | DACB |
| B | 4 787.213 | 3 | 1 595.738 | 33.598 | 0** | ||
| C | 13 474.354 | 3 | 4 491.451 | 94.567 | 0** | ||
| D | 22 480.702 | 3 | 7 493.567 | 157.776 | 0** | ||
| Residual | 3 467.127 | 73 | 47.495 | ||||
| R2=0.947 | |||||||
| 7 d flexural strength | A | 25.727 | 3 | 8.576 | 9.715 | 0** | DAB |
| B | 22.451 | 3 | 7.484 | 8.477 | 0.001** | ||
| C | 3.393 | 3 | 1.131 | 1.281 | 0.309 | ||
| D | 73.717 | 3 | 24.572 | 27.835 | 0** | ||
| Residual | 16.773 | 19 | 0.883 | ||||
| R2=0.889 | |||||||
| 28 d flexural strength | A | 27.500 | 3 | 9.167 | 5.329 | 0.008** | DAB |
| B | 24.330 | 3 | 8.110 | 4.715 | 0.013* | ||
| C | 6.366 | 3 | 2.122 | 1.234 | 0.327 | ||
| D | 93.148 | 3 | 31.049 | 18.050 | 0** | ||
| Residual | 30.963 | 18 | 1.720 | ||||
| R2=0.842 | |||||||
| Performance | Evaluation index | Indicator type | Optimal combination | Factor order | Selected main factor and level | |||
|---|---|---|---|---|---|---|---|---|
| Range analysis | ANOVA | Comparison | ||||||
| Workability | Fluidity | Larger-the-better | A4B4C4D3 | ACBD | ACBD | Same | A4C3 | |
| Setting time | Initial | Nominal-the-better | A3B3C2D2 | CABD | CABD | Same | ||
| Final | Nominal-the-better | A3B3C2D2 | CABD | CABD | Same | |||
| Volume stability | Drying shrinkage rate | 7 d | Smaller-the-better | A2B3C1D3 | CBDA | CDBA | Difference | C1B3 |
| 28 d | Smaller-the-better | A2B3C1D4 | CBAD | CBAD | Same | |||
| Mechanical property | Compressive strength | 7 d | Larger-the-better | A1B2C4D1 | DCAB | DACB | Difference | D1A1 |
| 28 d | Larger-the-better | A1B2C4D2 | DACB | DACB | Same | |||
| Flexural strength | 7 d | Larger-the-better | A1B2C3D1 | DBAC | DAB | Difference | ||
| 28 d | Larger-the-better | A1B2C3D1 | DABC | DAB | Same | |||
表10 各指标极差和方差分析结果
Table 10 Range and variance analysis results for each index
| Performance | Evaluation index | Indicator type | Optimal combination | Factor order | Selected main factor and level | |||
|---|---|---|---|---|---|---|---|---|
| Range analysis | ANOVA | Comparison | ||||||
| Workability | Fluidity | Larger-the-better | A4B4C4D3 | ACBD | ACBD | Same | A4C3 | |
| Setting time | Initial | Nominal-the-better | A3B3C2D2 | CABD | CABD | Same | ||
| Final | Nominal-the-better | A3B3C2D2 | CABD | CABD | Same | |||
| Volume stability | Drying shrinkage rate | 7 d | Smaller-the-better | A2B3C1D3 | CBDA | CDBA | Difference | C1B3 |
| 28 d | Smaller-the-better | A2B3C1D4 | CBAD | CBAD | Same | |||
| Mechanical property | Compressive strength | 7 d | Larger-the-better | A1B2C4D1 | DCAB | DACB | Difference | D1A1 |
| 28 d | Larger-the-better | A1B2C4D2 | DACB | DACB | Same | |||
| Flexural strength | 7 d | Larger-the-better | A1B2C3D1 | DBAC | DAB | Difference | ||
| 28 d | Larger-the-better | A1B2C3D1 | DABC | DAB | Same | |||
| Goal level | Criteria level (First-level index) | Index level (Second-level indicator) |
|---|---|---|
| Comprehensive performance of grouting materials G | Workability F1 | Fluidity S1 |
| Initial setting time S2 | ||
| Final setting time S3 | ||
| Volume stability F2 | 7 d drying shrinkage rate S4 | |
| 28 d drying shrinkage rate S5 | ||
| Mechanical property F3 | 7 d compressive strength S6 | |
| 28 d compressive strength S7 | ||
| 7 d flexural strength S8 | ||
| 28 d flexural strength S9 |
表11 注浆材料综合性能评价指标体系
Table 11 Comprehensive performance evaluation index system of grouting materials
| Goal level | Criteria level (First-level index) | Index level (Second-level indicator) |
|---|---|---|
| Comprehensive performance of grouting materials G | Workability F1 | Fluidity S1 |
| Initial setting time S2 | ||
| Final setting time S3 | ||
| Volume stability F2 | 7 d drying shrinkage rate S4 | |
| 28 d drying shrinkage rate S5 | ||
| Mechanical property F3 | 7 d compressive strength S6 | |
| 28 d compressive strength S7 | ||
| 7 d flexural strength S8 | ||
| 28 d flexural strength S9 |
| Level | F1 | F2 | F3 | Comprehensive weight | Ranking |
|---|---|---|---|---|---|
| 0.380 8 | 0.107 0 | 0.512 2 | |||
| S1 | 0.560 1 | 0.213 3 | 2 | ||
| S2 | 0.338 3 | 0.128 8 | 3 | ||
| S3 | 0.101 6 | 0.038 7 | 7 | ||
| S4 | 0.182 9 | 0.019 6 | 9 | ||
| S5 | 0.817 1 | 0.087 4 | 5 | ||
| S6 | 0.159 4 | 0.081 6 | 6 | ||
| S7 | 0.546 7 | 0.280 0 | 1 | ||
| S8 | 0.065 4 | 0.033 5 | 8 | ||
| S9 | 0.228 5 | 0.117 0 | 4 |
表12 评价指标综合权重
Table 12 Comprehensive weight of evaluation index
| Level | F1 | F2 | F3 | Comprehensive weight | Ranking |
|---|---|---|---|---|---|
| 0.380 8 | 0.107 0 | 0.512 2 | |||
| S1 | 0.560 1 | 0.213 3 | 2 | ||
| S2 | 0.338 3 | 0.128 8 | 3 | ||
| S3 | 0.101 6 | 0.038 7 | 7 | ||
| S4 | 0.182 9 | 0.019 6 | 9 | ||
| S5 | 0.817 1 | 0.087 4 | 5 | ||
| S6 | 0.159 4 | 0.081 6 | 6 | ||
| S7 | 0.546 7 | 0.280 0 | 1 | ||
| S8 | 0.065 4 | 0.033 5 | 8 | ||
| S9 | 0.228 5 | 0.117 0 | 4 |
| First-level index | Second-level index | AHP weight wj | Entropy method weight vj | Combined weight wj* | Ranking |
|---|---|---|---|---|---|
| Workability F1 | Fluidity S1 | 0.213 3 | 0.043 6 | 0.085 3 | 5 |
| Initial setting time S2 | 0.128 8 | 0.125 7 | 0.148 6 | 3 | |
| Final setting time S3 | 0.038 7 | 0.140 3 | 0.049 8 | 7 | |
| Volume stability F2 | 7 d drying shrinkage rate S4 | 0.019 6 | 0.060 1 | 0.010 8 | 9 |
| 28 d drying shrinkage rate S5 | 0.087 4 | 0.070 0 | 0.056 1 | 6 | |
| Mechanical properties F3 | 7 d compressive strength S6 | 0.081 6 | 0.144 4 | 0.108 1 | 4 |
| 28 d compressive strength S7 | 0.280 0 | 0.134 6 | 0.345 8 | 1 | |
| 7 d flexural strength S8 | 0.033 5 | 0.139 2 | 0.042 8 | 8 | |
| 28 d flexural strength S9 | 0.117 0 | 0.142 1 | 0.152 6 | 2 |
表13 基于AHP-熵值法的注浆材料综合性能评价指标组合权重
Table 13 Combined weight of comprehensive performance evaluation index of grouting materials based on AHP-entropy method
| First-level index | Second-level index | AHP weight wj | Entropy method weight vj | Combined weight wj* | Ranking |
|---|---|---|---|---|---|
| Workability F1 | Fluidity S1 | 0.213 3 | 0.043 6 | 0.085 3 | 5 |
| Initial setting time S2 | 0.128 8 | 0.125 7 | 0.148 6 | 3 | |
| Final setting time S3 | 0.038 7 | 0.140 3 | 0.049 8 | 7 | |
| Volume stability F2 | 7 d drying shrinkage rate S4 | 0.019 6 | 0.060 1 | 0.010 8 | 9 |
| 28 d drying shrinkage rate S5 | 0.087 4 | 0.070 0 | 0.056 1 | 6 | |
| Mechanical properties F3 | 7 d compressive strength S6 | 0.081 6 | 0.144 4 | 0.108 1 | 4 |
| 28 d compressive strength S7 | 0.280 0 | 0.134 6 | 0.345 8 | 1 | |
| 7 d flexural strength S8 | 0.033 5 | 0.139 2 | 0.042 8 | 8 | |
| 28 d flexural strength S9 | 0.117 0 | 0.142 1 | 0.152 6 | 2 |
| Group | AHP | Entropy method | AHP-entropy method | |||
|---|---|---|---|---|---|---|
| Evaluation value | Ranking | Evaluation value | Ranking | Evaluation value | Ranking | |
| 1 | 0.080 | 4 | 0.101 | 2 | 0.094 | 3 |
| 2 | 0.092 | 2 | 0.097 | 3 | 0.106 | 2 |
| 3 | 0.079 | 5 | 0.071 | 6 | 0.084 | 5 |
| 4 | 0.058 | 10 | 0.054 | 11 | 0.063 | 10 |
| 5 | 0.029 | 14 | 0.029 | 13 | 0.022 | 13 |
| 6 | 0.017 | 16 | 0.016 | 16 | 0.010 | 16 |
| 7 | 0.085 | 3 | 0.079 | 5 | 0.088 | 4 |
| 8 | 0.076 | 6 | 0.070 | 7 | 0.078 | 6 |
| 9 | 0.040 | 12 | 0.035 | 12 | 0.030 | 12 |
| 10 | 0.074 | 8 | 0.068 | 8 | 0.074 | 8 |
| 11 | 0.051 | 11 | 0.056 | 9 | 0.048 | 11 |
| 12 | 0.074 | 7 | 0.086 | 4 | 0.078 | 7 |
| 13 | 0.071 | 9 | 0.055 | 10 | 0.070 | 9 |
| 14 | 0.114 | 1 | 0.137 | 1 | 0.121 | 1 |
| 15 | 0.034 | 13 | 0.028 | 14 | 0.021 | 14 |
| 16 | 0.026 | 15 | 0.017 | 15 | 0.013 | 15 |
表14 综合评估值
Table 14 Comprehensive assessment value
| Group | AHP | Entropy method | AHP-entropy method | |||
|---|---|---|---|---|---|---|
| Evaluation value | Ranking | Evaluation value | Ranking | Evaluation value | Ranking | |
| 1 | 0.080 | 4 | 0.101 | 2 | 0.094 | 3 |
| 2 | 0.092 | 2 | 0.097 | 3 | 0.106 | 2 |
| 3 | 0.079 | 5 | 0.071 | 6 | 0.084 | 5 |
| 4 | 0.058 | 10 | 0.054 | 11 | 0.063 | 10 |
| 5 | 0.029 | 14 | 0.029 | 13 | 0.022 | 13 |
| 6 | 0.017 | 16 | 0.016 | 16 | 0.010 | 16 |
| 7 | 0.085 | 3 | 0.079 | 5 | 0.088 | 4 |
| 8 | 0.076 | 6 | 0.070 | 7 | 0.078 | 6 |
| 9 | 0.040 | 12 | 0.035 | 12 | 0.030 | 12 |
| 10 | 0.074 | 8 | 0.068 | 8 | 0.074 | 8 |
| 11 | 0.051 | 11 | 0.056 | 9 | 0.048 | 11 |
| 12 | 0.074 | 7 | 0.086 | 4 | 0.078 | 7 |
| 13 | 0.071 | 9 | 0.055 | 10 | 0.070 | 9 |
| 14 | 0.114 | 1 | 0.137 | 1 | 0.121 | 1 |
| 15 | 0.034 | 13 | 0.028 | 14 | 0.021 | 14 |
| 16 | 0.026 | 15 | 0.017 | 15 | 0.013 | 15 |
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