复掺粉煤灰与矿渣粉的混凝土自收缩预测模型

doi:10.16552/j.cnki.issn1001-1625.2025.1238

摘要/Abstract

摘要：

为准确预测粉煤灰（FA）与矿渣粉（GGBS）复掺对混凝土早期自收缩行为的影响，本文通过试验系统研究了FA与GGBS总掺量为20%、30%、40%和50%（质量分数），以及FA与GGBS掺入比分别为3∶0、3∶1、3∶2、3∶3（质量比）的共计16组配合比混凝土的自收缩发展规律，基于此建立了相应的自收缩预测模型。结果表明：当FA与GGBS掺入比固定时，混凝土自收缩率随掺合料总掺量的增加而降低；当总掺量不变时，自收缩率随GGBS占比提高而显著增大。灰色关联分析进一步表明，FA掺量是影响自收缩的主导因素，其影响程度高于GGBS。在此基础上，本文对经典混凝土自收缩模型（B4模型）进行了修正，引入了表征复掺效应的修正项K_fs，并采用了与最终自收缩值相关的时间发展指数n_fs，从而构建了一个适用于FA与GGBS复掺混凝土的自收缩预测模型。经验证，该模型预测结果与试验数据吻合良好，可为相关工程中混凝土自收缩预测提供理论依据。

关键词: 混凝土, 自收缩, 粉煤灰, 矿渣粉, 预测模型

Abstract:

To accurately predict the influence of combined incorporation of fly ash （FA） and ground granulated blast-furnace slag powder （GGBS） on the early-age autogenous shrinkage behavior of concrete， this study systematically investigated the development of autogenous shrinkage in 16 concrete mixtures with total replacement levels of 20%， 30%， 40%， and 50% （mass fraction） by FA and GGBS， and FA-to-GGBS blending ratios of 3∶0， 3∶1， 3∶2， and 3∶3 （mass ratio）. Based on the experimental results， a corresponding prediction model for autogenous shrinkage was established. The results indicate that when the FA-to-GGBS blending ratio is fixed， the autogenous shrinkage rate of concrete decreases with the increase in the total replacement level of mineral admixtures. Conversely， with a constant total replacement level， the autogenous shrinkage increases significantly as the proportion of GGBS rises. Grey relational analysis further reveals that the FA content is the dominant factor influencing autogenous shrinkage， with a greater impact than GGBS. Building on these findings， this study modifies the classical B4 model for concrete autogenous shrinkage by introducing a correction term K_fs to characterize the effect of combined incorporation of FA and GGBS and adopting a time-development exponent n_fs related to the ultimate autogenous shrinkage. Thus， a prediction model suitable for concrete incorporating both FA and GGBS is established. Validation results demonstrate that the model predictions agree well with experimental data， providing a theoretical basis for predicting autogenous shrinkage in related engineering applications.

Key words: concrete, autogenous shrinkage, fly ash, ground granulated blast-furnace slag powder, prediction model

中图分类号:

TU528

古盛斌, 李北星, 翁贤杰, 田沈华. 复掺粉煤灰与矿渣粉的混凝土自收缩预测模型[J]. 硅酸盐通报, 2026, 45(6): 2011-2020.

GU Shengbin, LI Beixing, WENG Xianjie, TIAN Shenhua. Prediction Model for Autogenous Shrinkage of Concrete with Combined Incorporation of Fly Ash and Ground Granulated Blast-Furnace Slag Powder[J]. BULLETIN OF THE CHINESE CERAMIC SOCIETY, 2026, 45(6): 2011-2020.

图/表 7

表1 胶凝材料的主要化学成分

Table 1 Main chemical composition of cementitious materials

Material	Mass fraction/%
Material	SiO₂	Al₂O₃	Fe₂O₃	CaO	MgO	Na₂O	K₂O	SO₃	LOI
P·O	17.59	4.58	5.33	60.62	2.67	0.09	0.68	2.65	3.33
FA	47.30	27.37	6.23	5.82	1.16	1.11	2.23	1.93	4.17
GGBS	32.48	13.45	0.45	42.07	7.79	0.42	0.53	0.87	0.74

表2 混凝土配合比

Table 2 Mix proportion of concrete

Mix ID	Materials dosage/（kg·m^-3）
Mix ID	P·O	FA	GGBS	RS	LCS	Water	PCA
F0S0	480	0	0	712	1 114	154	5.28
F20S0	384	96.0	0	712	1 114	154	5.28
F15S5	384	72.0	24.0	712	1 114	154	5.28
F12S8	384	57.6	38.4	712	1 114	154	5.28
F10S10	384	48.0	48.0	712	1 114	154	5.28
F30S0	336	144.0	0	712	1 114	154	5.28
F22.5S7.5	336	108.0	36.0	712	1 114	154	5.28
F18S12	336	86.4	57.6	712	1 114	154	5.28
F15S15	336	72.0	72.0	712	1 114	154	5.28
F40S0	288	192.0	0	712	1 114	154	5.28
F30S10	288	144.0	48.0	712	1 114	154	5.28
F24S16	288	115.2	76.8	712	1 114	154	5.28
F20S20	288	96.0	96.0	712	1 114	154	5.28
F50S0	240	240.0	0	712	1 114	154	5.28
F37.5S12.5	240	180.0	60.0	712	1 114	154	5.28
F30S20	240	144.0	96.0	712	1 114	154	5.28
F25S25	240	120.0	120.0	712	1 114	154	5.28

图1 不同FA和GGBS掺量下混凝土的自收缩率

Fig.1 Autogenous shrinkage ratio of concrete with different replacement levels of FA and GGBS

图2 灰色关联系数的计算结果

Fig.2 Calculation results of grey relational coefficients

表3 灰色关联度计算结果

Table 3 Calculation results of grey relational grades

Relational degree and ranking	FA content	GGBS content
3 d relational degree	0.568	0.512
3 d relational degree ranking	1	2
28 d relational degree	0.659	0.626
28 d relational degree ranking	1	2

表4 K?fs的拟合结果

Table 4 Fitting results of K?fs

Fitting result	R²
$K f s = 1.527 6 β 2 - 2.780 1 β λ - 2.085 0 β + 4.048 4 λ 2 + 0.362 4 λ + 0.993 5$	0.975 5
$K f s = e - 2.253 9 β + 1.039 1 λ$	0.932 5
$K f s = - 1.331 6 β 0.478 2 + β + 7.886 3 λ 9.853 1 + λ + 1.000 1$	0.930 8

表4 K?fs的拟合结果

Table 4 Fitting results of K?fs

Fitting result	R²
$K f s = 1.527 6 β 2 - 2.780 1 β λ - 2.085 0 β + 4.048 4 λ 2 + 0.362 4 λ + 0.993 5$	0.975 5
$K f s = e - 2.253 9 β + 1.039 1 λ$	0.932 5
$K f s = - 1.331 6 β 0.478 2 + β + 7.886 3 λ 9.853 1 + λ + 1.000 1$	0.930 8

图3 混凝土自收缩真实值与预测值的对比

Fig.3 Comparison between true and predicted values of concrete autogenous shrinkage

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