# Effect of Fibre Reinforcement on Creep in Early Age Concrete

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

^{3}, obtained according to UNE 80103:2013 [25]. The quantity of cement used was 390 kg/m

^{3}and its composition can be seen in Table 2. A superplasticizer additive, Master Ease 5025, was added in the proportion of 1% wt. of cement.

#### 2.2. Methods

#### 2.2.1. Compressive Strength

^{3}, cured in a humidity chamber under controlled conditions (20 ± 2 °C and 95 ± 5% humidity).

#### 2.2.2. Creep Test

#### 2.2.3. Modulus of Elasticity

#### 2.2.4. Delayed Elastic Strain

#### 2.2.5. Microscopic Analysis

## 3. Results and Discussion

#### 3.1. Compressive Strength

#### 3.2. Creep Test

#### 3.2.1. Proposed Creep Formulation

- -
- σ(to) is stress on specimens during creep test.
- -
- E
_{c,to}is the initial modulus of elasticity in specimens. - -
- E
_{c}_{,28}is the modulus of elasticity of the specimens at 28 days. - -
- φ
_{HR}is the coefficient of influence of relative humidity [22]. - -
- -
- α(t
_{0}) is the coefficient associated with the loading age proposed by the authors; - -
- α(t − t
_{0}) is the coefficient associated with the evolution of creep with time proposed by the authors.

_{0})” and “α(t − t

_{0})”, while Figure 8 shows the range of optimal coefficients of the model proposed by the authors to minimize the deviation of the predictive model compared with the experimental results obtained in the laboratory.

_{0}) = 0.13; α(t − t

_{0}) = 0.39.

#### 3.2.2. Verification of Creep Formulation

#### 3.3. Modulus of Elasticity

#### 3.4. Delayed Elastic Strain

- -
- ɛ
_{e,i}is the instantaneous elastic strain. - -
- ɛ
_{e,d}is the delayed elastic strain. - -
- t
_{d}is the unloading age. - -
- E
_{c,td}is the modulus of elasticity of the specimens at unloading age.

#### 3.5. Microscopic Analysis

## 4. Conclusions

- -
- From the analysis of the creep strain undergone by the FRC specimens analysed during the test, two stages can be distinguished: (a) in a first stage, the creep deformation of the specimens loaded at an earlier age shows a greater strain; (b) in the second stage, the creep strain is equalized for the different loading ages.
- -
- The strain undergone by FRC specimens loaded at an earlier age, 24 h after their manufacture, shows a much lower level than predicted by the formulation proposed by the EHE-08 standard. In the case of the specimens loaded at the ages of three, seven and twenty-eight days, the strain is also less than that foreseen in the EHE-08 standard, although the difference is not so high.
- -
- The authors propose an adjustment of the creep coefficients proposed in the EHE-08 equation associated with the loading age β(t
_{0}) and the evolution of the creep in time βc(t − t_{0}). - -
- From a comparative analysis of the stress/strain curves of the FRC specimens during their loading and unloading, it can be concluded that the FRC loaded at an earlier age stiffens after a creep episode.
- -
- Once the results of the creep test of FRC loaded at different ages was analysed, it could be concluded that FRC had better creep behaviour than conventional concrete.
- -
- Analysing the evolution of the delayed elastic deformation of the FRC specimens after the end of the creep test, it is concluded that, the FRC loaded at an earlier age, undergoes less deformation.
- -
- The authors propose a formulation for the analysis of the delayed elastic deformation of FRC after a creep episode.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Evolution of creep deformation undergone by FRC: (

**a**) specimens loaded at 15 MPa; (

**b**) specimens loaded at 20 MPa.

**Figure 7.**Analysis of the error induced by the variation of the exponent of the creep coefficients α(t

_{0}) and α(t − t

_{0}) in the model proposed by the authors to determine the creep strain undergone by FRC: (

**a**) FRC specimens loaded at 24 h (

**a**); at 3 d (

**b**); at 7 d (

**c**); and at 28 d (

**d**).

**Figure 8.**Optimization of the coefficients “α(t

_{0})” and “α(t − t

_{0})” of the model proposed by the authors for calculating the creep strain of FRC.

**Figure 9.**Creep deformation undergone by FRC specimens: FRC loaded at 24 h (

**a**); (

**b**) 3 d; (

**c**) 7 d; (

**d**) 28 d.

**Figure 10.**Tension-deformation curve during loading of the specimens: (

**a**) FRC specimens loaded at 15 MPa; (

**b**) FRC specimens loaded at 20 MPa.

**Figure 12.**Stress/strain curve during the unloading of the specimens: (

**a**) FRC specimens loaded at 15 MPa; (

**b**) FRC specimens loaded at 20 MPa.

**Figure 15.**Evolution of the elastic strain of FRC after a creep episode. Experimental strain versus strain predicted by the model proposed by the authors: FRC specimens loaded at (

**a**) 24 h; (

**b**) 3 d; (

**c**) 7 d; (

**d**) 28 d.

Fraction of Aggregate | Absorption [wt.%] | Density [kg/m^{3}] | Sand Equivalent |
---|---|---|---|

FA0-2 | 0.49 | 2690 | >75 |

FA0-4 | 0.49 | 2690 | >80 |

CA4-12 | 0.54 | 2700 | - |

CA10-20 | 0.54 | 2680 | - |

Fe_{2}O_{3} | CaO | SiO_{2} | Al_{2}O_{3} | MgO | TiO_{2} | SO_{3} | K_{2}O | Others | |
---|---|---|---|---|---|---|---|---|---|

Compound [wt.%] | 3.38 | 66.60 | 17.81 | 4.79 | 1.30 | 0.20 | 4.49 | 0.78 | <0.5 |

Material | Mix [kg/m^{3}] |
---|---|

FA0-2 | 480 |

FA0-4 | 480 |

CA4-12 | 480 |

CA10-20 | 480 |

Cement | 390 |

Water | 165 |

Additive Master Ease 5025 | 3.9 (1% wt. cement) |

Fibres | 35 |

w/c | 0.45 |

Specimen Code | Group | Loading Age [d] | Test Load [kN] | Test Stress [MPa] |
---|---|---|---|---|

CF-1 | 1 | 1 | 265 | 15 |

CF-2 | 1 | 1 | 265 | 15 |

CF-3 | 2 | 3 | 265 | 15 |

CF-4 | 2 | 3 | 265 | 15 |

CF-5 | 3 | 7 | 353 | 20 |

CF-6 | 3 | 7 | 353 | 20 |

CF-7 | 4 | 28 | 353 | 20 |

CF-8 | 4 | 28 | 353 | 20 |

**Table 5.**Evolution of the modulus of elasticity of FRC after a creep episode. Initial “Eo” and residual “Er” modulus of elasticity.

Loading Age (d) | Eo (GPa) | Er (GPa) |
---|---|---|

1 | 21.913 | 41.712 |

3 | 33.500 | 38.842 |

7 | 33.667 | 33.904 |

28 | 36.100 | 34.918 |

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**MDPI and ACS Style**

González, L.; Gaute, Á.; Rico, J.; Thomas, C.
Effect of Fibre Reinforcement on Creep in Early Age Concrete. *Appl. Sci.* **2022**, *12*, 257.
https://doi.org/10.3390/app12010257

**AMA Style**

González L, Gaute Á, Rico J, Thomas C.
Effect of Fibre Reinforcement on Creep in Early Age Concrete. *Applied Sciences*. 2022; 12(1):257.
https://doi.org/10.3390/app12010257

**Chicago/Turabian Style**

González, Laura, Álvaro Gaute, Jokin Rico, and Carlos Thomas.
2022. "Effect of Fibre Reinforcement on Creep in Early Age Concrete" *Applied Sciences* 12, no. 1: 257.
https://doi.org/10.3390/app12010257