# The Influence of Fly Ash on the Tensile Creep Prediction of High-Strength Concrete at Early Ages

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

**q**of the ZC model was introduced in order to characterize the influence of fly ash on the paste at early ages. Therefore, this paper demonstrated both theoretically and experimentally that the ZC model can better predict the early-age TC of HSC with fly ash.

## 1. Introduction

## 2. Prediction Models of Early-Age TC Considering the Paste Property

**r**and

**q**) were introduced to the ZC model, which were quite significant in predicting the accuracy of the early-age concrete TC. It was found that the parameter

**r**was stabilized at 0.4 for different loading ages and the FA contents in the previous study by Yang’s research team [7,24]. So, the effect of FA on creep is mainly reflected by parameter

**q**.

## 3. Raw Materials and Experimental Methods

#### 3.1. Raw Materials and Mix Proportion

^{3}, and it met the requirements of pumping concrete according to the Chinese standard JGJ/T 10-2011 (Technical Specification for Concrete Pumping Construction). The river sand was used as fine aggregate; the fineness modulus was 2.40, and it had an apparent density of 2630 kg/m

^{3}. The poly-carboxylate super-plasticizer with a 30% water-reducing rate was used as water reducing agent.

#### 3.2. Basic Experimental Parameters and Mechanical Property Index Stress Level Determination

#### 3.2.1. Stress Level Determination

#### 3.2.2. Loading Ages

#### 3.3. Tensile Creep Test Method

#### 3.3.1. Specimen Size

#### 3.3.2. Curing Temperature Condition

#### 3.3.3. Test Procedure

**ε**) can be obtained from Equation 4:

_{tensile creep}**ε**(=

_{B}**ε**),

_{total}**ε**

_{A}(=

**ε**

_{as}+

**ε**

_{T}), and

**ε**, were obtained by experimental measurements.

_{elastic}## 4. Applicability Analysis of Different Six Creep Models

#### 4.1. Calculation Parameters of Six Creep Models

#### 4.2. Calculation Parameters of Six Creep Models

#### 4.3. Prediction Accuracy Analysis of Six Creep Models

## 5. Discussion

**r**and

**q**) were introduced to the ZC model, and the stiffness of Spring C and the viscosity coefficient of Dashpot C were set to change with time, which reflected the process of concrete performance change at the early age. Because the structural composition and hardening process were considered in the ZC model, it is more accurate at reflecting the early-age tensile creep of HSC containing FA.

## 6. Conclusions

- (1)
- The TC was significantly affected at early ages by the paste properties development and the FA. The rate of TC development was faster when the loading age was greater.
- (2)
- The comparison results between the tensile creep experimental values and the model predictions values of HSC with 30% FA of tensile creep and the model predictions showed that the errors of BP-2, B-3, MC2010, ACI 209R, and GL 2000 models were relatively larger than ZC model, especially when loading age was less than 3d.
- (3)
- The ZC model can be developed to consider the time-dependent property of a paste containing FA. The parameter
**q**was introduced in order to reflect the influence of FA on paste, and it agreed well with the experimental values of early-age TC of HSC containing FA. - (4)
- The effect of different types of SCMs on paste properties is different. The applicability of the TC prediction model to HSC containing other SCMs remains to be further investigated. A more comprehensive concrete creep prediction model could be useful for concrete production requirements.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Powder particle size distribution and FA’s SEM image: (

**a**) Powders’ particle size distribution; (

**b**) FA’s SEM image.

Factors | Model | ||||||
---|---|---|---|---|---|---|---|

ZC | BP-2 | B-3 | MC2010 | ACI209R | GL2000 | ||

Internal factors | Mass of aggregate | ● | ● | ||||

Air content | ● | ● | |||||

FA | ● | ||||||

Cement type | ● | ● | ● | ● | ● | ● | |

The specific gravity of the fine aggregate | ● | ● | |||||

Slump | ● | ||||||

Water-binder ratio | ● | ● | |||||

External factors | Loading age | ● | ● | ● | ● | ● | ● |

Calculating age | ● | ● | ● | ● | ● | ● | |

Stress | ● | ● | ● | ● | ● | ● | |

Cross-section shape | ● | ||||||

28d strength | ● | ● | ● | ● | ● | ● | |

Cross section size | ● | ● | ● | ● | ● | ● | |

28d Elastic modulus | ● | ● | ● | ● | |||

Ambient humidity | ● | ● | ● | ● | ● | ● | |

Ambient temperature | ● | ● | |||||

Drying age | ● |

Materials | Index | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Chemical Composition (%) | Physical Properties | |||||||||||

SiO_{2} | Al_{2}O_{3} | Cao | Fe_{2}O_{3} | Na_{2}O | MgO | SO_{3} | K_{2}O | Specific Surface Area (m ^{2}/cm^{3}) | Density (g/cm ^{3}) | Ignition Loss (%) | Average Grain Size (μm) | |

Cement | 24.95 | 6.99 | 54.33 | 2.83 | 0.21 | 2.16 | 2.89 | 0.66 | 368 | 2.99 | 3.66 | 26.04 |

FA | 46.6 | 41.4 | 3.18 | 3.90 | 0.00 | 0.22 | 0.61 | 0.72 | 337 | 2.03 | 4.79 | 62.12 |

Cement | Fly Ash | Sand | Coarse Aggregate | Superplasticizer | Water |
---|---|---|---|---|---|

391 | 167 | 687 | 988 | 11 | 167 |

**Table 4.**Basic parameters of TC experiments and mechanical properties of HSC. (

**W/B**= 0.3, FA = 30wt %).

Loading Age (d) | Applied Load (kN) | Splitting Tensile Strength (MPa) | Compression Strength (Mpa) | Tensile Modulus of Elasticity (Gpa) |
---|---|---|---|---|

1 | 5.99 | 1.27 | 9.81 | 21.67 |

2 | 12.77 | 2.71 | 27.55 | 29.02 |

3 | 15.03 | 3.19 | 31.50 | 33.11 |

5 | 17.52 | 3.72 | 42.67 | 37.10 |

7 | 18.36 | 3.90 | 51.91 | 40.09 |

ZC model | $\begin{array}{l}{t}_{0}\\ \left(\mathrm{d}\right)\end{array}$ | $\begin{array}{c}1/\chi \phi \\ ({10}^{-6}/MPa)\end{array}$ | $\phi $ | $\begin{array}{c}1/({E}_{V}+{E}_{H})\\ ({10}^{-6}/MPa)\end{array}$ | ${E}_{H}/{E}_{V}$ | $q$ | |

1 | 214.65 | 0.33 | 61.36 | 22.74 | 2.76 | ||

2 | 88.04 | 0.20 | 14.60 | 17.57 | 4.78 | ||

3 | 47.03 | 0.11 | 6.20 | 10.86 | 6.52 | ||

5 | 38.54 | 0.06 | 5.27 | 6.42 | 7.52 | ||

7 | 36.24 | 0.06 | 5.87 | 5.98 | 7.90 | ||

BP-2 model | $\begin{array}{l}{t}_{0}\\ \left(\mathrm{d}\right)\end{array}$ | $B$ | $m$ | $n$ | $E\prime /GPa$ | ||

1 | 1.49 | 0.29 | 0.28 | 21.31 | |||

2 | 1.49 | 0.29 | 0.28 | 39.13 | |||

3 | 1.49 | 0.29 | 0.28 | 50.58 | |||

5 | 1.49 | 0.29 | 0.28 | 50.81 | |||

7 | 1.49 | 0.29 | 0.28 | 56.88 | |||

B-3 model | $\begin{array}{l}{t}_{0}\\ \left(\mathrm{d}\right)\end{array}$ | $r({t}_{0})$ | $Q({t}_{0})f$ | ${q}_{2}$ of Modified B-3 model | |||

1 | 9.70 | 0.77 | 566.75 | ||||

2 | 9.85 | 0.57 | 332.44 | ||||

3 | 9.94 | 0.48 | 292.18 | ||||

5 | 10.06 | 0.39 | 266.37 | ||||

7 | 10.15 | 0.33 | 256.65 | ||||

$w/c$ | $a/c$ | $c(Kg/{m}^{3})$ | ${q}_{2}$ | ${q}_{3}$ | ${q}_{4}$ | ||

0.43 | 4.28 | 391.00 | 235.20 | 2.27 | 0.05 | ||

MC2010 model | $\begin{array}{l}{t}_{0}\\ \left(\mathrm{d}\right)\end{array}$ | $\beta ({t}_{0})$ | |||||

1 | 0.91 | ||||||

2 | 0.80 | ||||||

3 | 0.74 | ||||||

5 | 0.68 | ||||||

7 | 0.64 | ||||||

$\beta ({f}_{cm})$ | ${\alpha}_{1}$ | ${\alpha}_{2}$ | ${\alpha}_{3}$ | ${\phi}_{H}$ | ${\beta}_{H}$ | ${E}_{c}(28)/GPa$ | |

1.98 | 0.60 | 0.87 | 0.70 | 1.35 | 294.43 | 44.07 | |

ACI209R model | S/(S + G) | γ_{φ} | Slump (mm) | γ_{s} | |||

0.41 | 0.88 | 250 | 1.48 | ||||

GL2000 model | ${t}_{0}\left(\mathrm{d}\right)$ | v/s (mm) | h | ||||

As others | 28.60 | 0.60 |

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## Share and Cite

**MDPI and ACS Style**

Yao, J.; Yao, S.; Huang, S.; Ni, T.; Jiang, C.; Yang, Y.; Kong, D.
The Influence of Fly Ash on the Tensile Creep Prediction of High-Strength Concrete at Early Ages. *Materials* **2023**, *16*, 1337.
https://doi.org/10.3390/ma16041337

**AMA Style**

Yao J, Yao S, Huang S, Ni T, Jiang C, Yang Y, Kong D.
The Influence of Fly Ash on the Tensile Creep Prediction of High-Strength Concrete at Early Ages. *Materials*. 2023; 16(4):1337.
https://doi.org/10.3390/ma16041337

**Chicago/Turabian Style**

Yao, Jikai, Shuifeng Yao, Senle Huang, Tongyuan Ni, Chenhui Jiang, Yang Yang, and Deyu Kong.
2023. "The Influence of Fly Ash on the Tensile Creep Prediction of High-Strength Concrete at Early Ages" *Materials* 16, no. 4: 1337.
https://doi.org/10.3390/ma16041337