Prediction Model for Autogenous Shrinkage of Concrete with Combined Incorporation of Fly Ash and Ground Granulated Blast-Furnace Slag Powder

doi:10.16552/j.cnki.issn1001-1625.2025.1238

Abstract

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

CLC Number:

TU528

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.

Figures/Tables 7

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

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

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

Fig.2 Calculation results of grey relational coefficients

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

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

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

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

References 31

[1]	ZHANG M H， TAM C T， LEOW M P. Effect of water-to-cementitious materials ratio and silica fume on the autogenous shrinkage of concrete［J］. Cement and Concrete Research， 2003， 33（10）： 1687-1694. DOI URL
[2]	黄从斌，邰洪生，罗居刚. 预湿生物炭对超高性能混凝土自收缩和抗压强度的影响［J］. 硅酸盐通报， 2025， 44（7）： 2458-2464. DOI
	HUANG C B， TAI H S， LUO J G. Effect of pre-wetted biochar on autogenous shrinkage and compressive strength of ultra-high performance concrete［J］. Bulletin of the Chinese Ceramic Society， 2025， 44（7）： 2458-2464 （in Chinese）. DOI
[3]	李景浩，何小波，胡少伟，等. 现代混凝土自收缩及其调控研究进展［J］. 水利水运工程学报， 2023（2）： 150-161.
	LI J H， HE X B， HU S W， et al. Advances in autogenous shrinkage and its regulation of modern concrete［J］. Hydro-Science and Engineering， 2023（2）： 150-161 （in Chinese）.
[4]	WEN C Y， SHEN D J， FENG Z Z， et al. Relationship between internal relative humidity and autogenous shrinkage of early-age concrete containing prewetted lightweight aggregates［J］. Structural Concrete， 2023， 24（3）： 4110-4125. DOI URL
[5]	CUI T T， NING B K， XIA X D， et al. Shrinkage prediction model of high strength lightweight aggregate concrete based on relative humidity［J］. Journal of Building Engineering， 2023， 75： 106932. DOI URL
[6]	LURA P， JENSEN O M， VAN BREUGEL K. Autogenous shrinkage in high-performance cement paste： an evaluation of basic mechanisms［J］. Cement and Concrete Research， 2003， 33（2）： 223-232. DOI URL
[7]	KHEIR J， KLAUSEN A， HAMMER T A， et al. Early age autogenous shrinkage cracking risk of an ultra-high performance concrete （UHPC） wall： modelling and experimental results［J］. Engineering Fracture Mechanics， 2021， 257： 108024. DOI URL
[8]	LIU J P， TIAN Q， WANG Y J， et al. Evaluation method and mitigation strategies for shrinkage cracking of modern concrete［J］. Engineering， 2021， 7（3）： 348-357. DOI URL
[9]	廖宜顺，魏小胜，左义兵. 粉煤灰掺量对水泥浆体电阻率与自收缩的影响［J］. 建筑材料学报， 2014， 17（3）： 517-520.
	LIAO Y S， WEI X S， ZUO Y B. Effect of fly ash content on electrical resistivity and autogenous shrinkage of cement paste［J］. Journal of Building Materials， 2014， 17（3）： 517-520 （in Chinese）.
[10]	花丽君，吴相豪，袁　潘. 掺粉煤灰和石灰粉影响再生混凝土自收缩变形的试验研究［J］. 粉煤灰， 2013， 25（1）： 37-39.
	HUA L J， WU X H， YUAN P. Experimental study of effects of fly ash and lime powder on autogenous shrinkage deformation of recycled concrete［J］. Coal Ash， 2013， 25（1）： 37-39 （in Chinese）.
[11]	TAZAWA E I， MIYAZAWA S. Influence of cement and admixture on autogenous shrinkage of cement paste［J］. Cement and Concrete Research， 1995， 25（2）： 281-287. DOI URL
[12]	JIANG Z W， SUN Z P， WANG P M. Autogenous relative humidity change and autogenous shrinkage of high-performance cement pastes［J］. Cement and Concrete Research， 2005， 35（8）： 1539-1545. DOI URL
[13]	LEE K M， LEE H K， LEE S H， et al. Autogenous shrinkage of concrete containing granulated blast-furnace slag［J］. Cement and Concrete Research， 2006， 36（7）： 1279-1285. DOI URL
[14]	TAZAWA E， MIYAZAWA S. Influence of constituents and composition on autogenous shrinkage of cementitious materials［J］. Magazine of Concrete Research， 1997， 49（178）： 15-22. DOI URL
[15]	EPPERS S， MUELLER C. On the examination of the autogenous shrinkage cracking propensity by means of the restrained ring test with particular consideration of the temperature influences［J］. VDZ Concrete Technology Reports， 2009（1）： 57-70.
[16]	YAN P， CHEN Z， WANG J， et al. Autogenous shrinkage of concrete prepared with the binders containing different kinds of mineral admixture［C］// Proceedings of the 12th International Conference on Chemistry of Cement， Canada， 2007： 1-8.
[17]	LAI M H， BINHOWIMAL S A M， GRIFFITH A M， et al. Shrinkage design model of concrete incorporating wet packing density［J］. Construction and Building Materials， 2021， 280： 122448. DOI URL
[18]	HUBLER M H， WENDNER R， BAŽANT Z P. Statistical justification of Model B4 for drying and autogenous shrinkage of concrete and comparisons to other models［J］. Materials and Structures， 2015， 48（4）： 797-814. DOI URL
[19]	RASOOLINEJAD M， RAHIMI-AGHDAM S， BAŽANT Z P. Prediction of autogenous shrinkage in concrete from material composition or strength calibrated by a large database， as update to model B4［J］. Materials and Structures， 2019， 52（2）： 33. DOI
[20]	LU T. Autogenous shrinkage of early age cement paste and mortar［D］. Delft： Delft University of Technology， 2019.
[21]	LU T S， LI Z M， HUANG H. Restraining effect of aggregates on autogenous shrinkage in cement mortar and concrete［J］. Construction and Building Materials， 2021， 289： 123166. DOI URL
[22]	LI Z. Autogenous shrinkage of alkali-activated slag and fly ash materials： from mechanism to mitigating strategies［D］. Delft： Delft University of Technology， 2021.
[23]	ZHANG H， WANG Y Y， LEHMAN D E， et al. Autogenous-shrinkage model for concrete with coarse and fine recycled aggregate［J］. Cement and Concrete Composites， 2020， 111： 103600. DOI URL
[24]	SHEN D J， WEN C Y， ZHU P F， et al. Influence of Barchip fiber on early-age autogenous shrinkage of high-strength concrete internally cured with super absorbent polymers［J］. Construction and Building Materials， 2020， 264： 119983. DOI URL
[25]	HU D K， HU N， BEN S J， et al. Multiscale prediction model for autogenous shrinkage of early-age concrete incorporating high volume fly ash［J］. Journal of Building Engineering， 2024， 98： 111281. DOI URL
[26]	许国东. 大掺量工业废渣混凝土早期开裂行为研究［D］. 南京：东南大学， 2018.
	XU G D. Studies on cracking behaviour of high volume slag and fly ash concrete at early age［D］. Nanjing： Southeast University， 2018 （in Chinese）.
[27]	毛思雨，姜东宇，袁龄卿，等. 基于微观视角分析高炉矿渣-粉煤灰替代水泥和矿粉体系的可行性［J］. 上海公路， 2025（3）： 143-150+155.
	MAO S Y， JIANG D Y， YUAN L Q， et al. Feasibility study of GGBFS-fly ash as a replacement for cement and mineral powder： a microstructural perspective［J］. Shanghai Highways， 2025（3）： 143-150+155 （in Chinese）.
[28]	郁浩安. 中高强复合粉煤灰-矿渣-尾矿混合砂混凝土基本性能研究［D］. 徐州：中国矿业大学， 2021.
	YU H A. Research on basic performance of medium and high strength composite fly ash-slag-tailing mixed sand concrete［D］. Xuzhou： China University of Mining and Technology， 2021 （in Chinese）.
[29]	闫博华，潘慧敏. 矿物掺合料对混凝土抗碳化性能影响的灰色关联分析［J］. 市政技术， 2024， 42（2）： 8-13.
	YAN B H， PAN H M. Grey correlation analysis of influence of mineral admixtures on concrete carbonation resistance［J］. Journal of Municipal Technology， 2024， 42（2）： 8-13 （in Chinese）.
[30]	WANG Q H， WANG Y Y， GENG Y， et al. Experimental study and prediction model for autogenous shrinkage of recycled aggregate concrete with recycled coarse aggregate［J］. Construction and Building Materials， 2021， 268： 121197. DOI URL
[31]	WENG J R， LIAO W C. Microstructure and shrinkage behavior of high-performance concrete containing supplementary cementitious materials［J］. Construction and Building Materials， 2021， 308： 125045. DOI URL