# Thermal Analysis of Mass Concrete Containing Ground Granulated Blast Furnace Slag

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Thermal Analysis

_{p}is the specific heat ($\frac{J}{kgK}$) and q

_{v}is the volumetric heat generation rate (W/m

^{3}).

^{3}), ${E}_{a}$ is the activation energy of the binder (J/mol), ${T}_{Ref}$ is the reference temperature ($296K)$ and $R$ is the gas constant ($8.314\frac{J}{molK}$).

_{3}S, C

_{2}S, C

_{3}A, and C

_{4}AF were calculated to be 60.13%, 12.95%, 7.27% and 9.71% by weight.

## 3. Experiments

_{2}= 31.3% by weight) [27]. Using the chemical composition of the Portland cement and Bogue’s equation, the ultimate heat of the Portland cement was calculated to be 485,101 J/kg. Then, with Equation (9), the ultimate heat of the binder in Table 1 was calculated to be 473,050 J/kg. Unlike the ultimate degree of hydration, the ultimate heat of the binder is solely dependent on the chemical composition of the cementitious material.

#### 3.1. Thermal Properties

#### 3.1.1. Activation Energy

#### 3.1.2. Adiabatic Temperature Rise

#### 3.1.3. Cube Testing (1.2-m)

## 4. Finite Element Analysis

#### 4.1. Verification of User Subroutines (DFLUX and USDFLD)

#### 4.2. Temperature Analysis

## 5. Sensitivity Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 13.**Finite element model at 16.50 h: Temperature (Red = high temperature, Blue = low temperature).

**Figure 14.**Comparison between FEM model prediction and measured temperatures at center (61.0-cm) and side surface (5.0-cm) for Batch 1.

**Figure 17.**Comparison of the temperature difference between FEM model and experiment: (

**a**) Batch 1, (

**b**) Batch 2 and (

**c**) Batch 3.

**Figure 18.**Temperature analysis sensitivity due to measured thermal properties: (

**a**) Thermal conductivity (Temperature) (

**b**) Thermal conductivity (Temperature difference), (

**c**) Activation energy (Temperature), (

**d**) Activation energy (Temperature difference), (

**e**) ATR (Temperature) and (

**f**) ATR (Temperature difference).

Material | Quantity (kg/m^{3}) |
---|---|

Cement | 150.7 |

GGBFS | 150.7 |

Water | 126.6 |

#57 Limestone Aggregate | 1064.9 |

Fine Aggregate | 809.2 |

Air entrainer (oz/cwt) | 0.65 |

Type B/D Water reducer/retarder (oz/cwt) | 3.0 |

w/cem | 0.42 |

Batch | Air Content, % | Slump, cm | Initial Temperature, °C |
---|---|---|---|

In-Lab | 6.0 | 13.3 | 21.66 |

Batch 1 | 5.5 | 12.7 | 26.0 |

Batch 2 | 6.5 | 20.3 | 29.0 |

Batch 3 | 6.8 | 15.2 | 22.0 |

Chemical Component | Portland Cement | Grade 100 GGBFS |
---|---|---|

CaO | 63.86% | 47.48% |

SiO_{2} | 20.34% | 28.89% |

Al_{2}O_{3} | 4.78% | 8.27% |

Fe_{2}O_{3} | 3.19% | 1.93% |

SO_{3} | 3.01% | 0.73% |

MgO | 2.41% | 8.34% |

Na_{2}O | 0.06% | - |

K_{2}O | 0.65% | 0.66% |

Blaine fineness $({m}^{2}/kg)$ | 372 | 325 |

Hydration Parameters | Two-Term | One-Term |
---|---|---|

${\alpha}_{u}^{1}$ | 0.56685 | 0.8552 |

${\tau}_{1}$ | 14.1090 | 28.62 |

${\beta}_{1}$ | 0.78485 | 0.609 |

${\alpha}_{u}^{2}$ | 0.28839 | - |

${\tau}_{2}$ | 166.985 | - |

${\beta}_{2}$ | 0.97925 | - |

${\alpha}_{u}^{T}$ | 0.8552 | 0.8552 |

Thermal Properties | ${\mathit{W}}_{\mathit{c}\mathit{e}\mathit{m}}$ $\left(\mathit{k}\mathit{g}/{\mathit{m}}^{3}\right)$ | ${\mathit{H}}_{\mathit{u}}$ $\left(\mathit{J}/\mathit{k}\mathit{g}\right)$ | ${\mathit{E}}_{\mathit{a}}$ $\left(\mathit{J}/\mathit{m}\mathit{o}\mathit{l}\right)$ | ${\mathit{K}}_{\mathit{u}}\left(\frac{\mathit{W}}{\mathit{m}\mathit{K}}\right)$ | ${\mathit{\alpha}}_{\mathit{u}}$ | $\frac{\mathit{w}}{\mathit{c}\mathit{e}\mathit{m}}$ |
---|---|---|---|---|---|---|

Value | 301.4 | 473,050 | 39,778 | 1.65 | 0.8552 | 0.42 |

Batch | Maximum Temperature (°C) | Maximum Temperature Difference (°C) | ||||
---|---|---|---|---|---|---|

Experiment | FEM Model | % Error | Experiment | FEM Model | % Error | |

1 | 50 at 20 h | 50.2 at 21.75 h | 0.4% | 18 at 21 h | 17.1 at 23.5 h | 0.56% |

2 | 53 at 20 h | 53.6 at 18.25 h | 1.13% | 20 at 20 h | 19.86 at 18 h | 0.7% |

3 | 44 at 20 h | 44.4 at 19.75 h | 0.91% | 16 at 19 h | 18.41 at 20 h | 15.1% |

Thermal Property | Maximum Temperature (°C) | Time of Maximum Temperature (hr) | Maximum Temperature Difference (°C) | Time of Maximum Temperature Difference (hr) |
---|---|---|---|---|

Thermal conductivity (±10%) | 44.4 ± 0.85 | 19.75 ± 1.0 | 18.41 ± 0.70 | 20.0 ± 0.25 |

Activation energy (±10%) | 44.4 ± 0.85 | 19.75 ± 0.0 | 18.41 ± 0.65 | 20.0 ± 0.00 |

ATR (±10%) | 44.4 ± 2.95 | 19.75 ± 0.25 | 18.41 ± 1.69 | 20.0 ± 0.00 |

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**MDPI and ACS Style**

Leon, G.; Chen, H.-L.
Thermal Analysis of Mass Concrete Containing Ground Granulated Blast Furnace Slag. *CivilEng* **2021**, *2*, 254-270.
https://doi.org/10.3390/civileng2010014

**AMA Style**

Leon G, Chen H-L.
Thermal Analysis of Mass Concrete Containing Ground Granulated Blast Furnace Slag. *CivilEng*. 2021; 2(1):254-270.
https://doi.org/10.3390/civileng2010014

**Chicago/Turabian Style**

Leon, Guadalupe, and Hung-Liang (Roger) Chen.
2021. "Thermal Analysis of Mass Concrete Containing Ground Granulated Blast Furnace Slag" *CivilEng* 2, no. 1: 254-270.
https://doi.org/10.3390/civileng2010014