# Optimization of Mass Concrete Construction Using a Twofold Parallel Genetic Algorithm

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## Abstract

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## 1. Introduction

## 2. Principles of the Thermo-Chemo-Mechanical Numerical Model

## 3. Optimization Problem of the Construction Phase of a Massive Concrete Structure Using a GA

#### 3.1. Design Variables

#### 3.2. Fitness Function

#### 3.3. Penalty Function

#### 3.4. Parallel Genetic Algorithm

## 4. Case Study

#### 4.1. Design Variables

**The type of concrete**$\left(T{y}_{c}\right)$: Four typical massive concrete mixes, taken from the data bank of the Laboratory of FURNAS [27], were elected as the possible choices for the present case study. FURNAS is the company responsible for the generation and distribution of electricity in the southeastern region of Brazil. Its data bank comprises comprehensive thermo-chemo-mechanical studies of more than 260 massive concrete mixes from some of the most important hydroelectric power plants in the world [28].

**The placing temperature:**the set defining the placing temperatures was defined as composed by 16 possible discrete placing temperatures. The minimum possible cooling temperature was considered to be ${P}_{{T}_{min}}=8{\phantom{\rule{3.33333pt}{0ex}}}^{\xb0}$C and the highest temperature was taken as the environmental average temperature, ${P}_{{T}_{max}}=26{\phantom{\rule{3.33333pt}{0ex}}}^{\xb0}$C. Therefore, the set of possible placing temperatures can be written as:

**The height of the lifts:**the following values were adopted for the height of lifts:

**The placing frequency:**the time required for treatment of the horizontal joints and also for dissipation of the heat released by the hydration reaction determines the placing schedule for pouring the subsequent lifts. For the case study here presented the following frequencies were adopted for placing the concrete lifts:

#### 4.2. Unitary Costs

#### 4.3. Control Parameters of the GA

#### 4.4. Results

#### 4.5. Speedups

#### 4.6. Validation

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Pseudocode of the Genetic Algorithm (gray background indicates that the steps are parallelized.

**Figure 8.**Temperature fields related to ages of 1, 3, 6, 7, 12 and 17 days for the optimal solution.

**Figure 12.**Speedup considering the parallel execution of the GA concerning the nodes number used to evaluate the individuals and based in a fixed number of eight processes of execution of the FEM program.

${\mathit{T}\mathit{y}}_{\mathit{c}}$ | Cement | Fly-Ash | Water | Fine Aggregate | Coarse Aggregate | Entrained Air | Retardant/Plasticizer |
---|---|---|---|---|---|---|---|

1 | 400.0 | 180 | 610.0 | 1193.0 | 0.080 | 0.800 | |

2 | 337.6 | 56.8 | 190 | 596.9 | 1124.0 | 0.105 | 0.844 |

3 | 229.2 | 50.3 | 187 | 629.7 | 1138.9 | 0.940 | 0.748 |

4 | 366.4 | 185 | 632.0 | 1204.0 | 0.841 |

${\mathit{T}\mathit{y}}_{\mathit{c}}$ | $\mathit{c}\mathit{\gamma}\mathbf{(}\mathbf{kJ}\mathbf{/}{\mathbf{m}}^{\mathbf{3}}\mathbf{\xb7}\mathbf{K}\mathbf{)}$ | k(W/m·K) | $\mathit{CTE}\mathbf{\left(}{\mathbf{10}}^{\mathbf{-}\mathbf{6}}{\mathbf{/}}^{\mathbf{\xb0}}\mathbf{C}\mathbf{\right)}$ | ${\mathit{f}}_{\mathit{t}\mathbf{,}\mathbf{\infty}}\mathbf{\left(}\mathbf{MPa}\mathbf{\right)}$ | ${\mathit{f}}_{\mathit{c}\mathbf{,}\mathbf{\infty}}\mathbf{\left(}\mathbf{MPa}\mathbf{\right)}$ | ${\mathit{E}}_{\mathbf{\infty}}\mathbf{\left(}\mathbf{MPa}\mathbf{\right)}$ |
---|---|---|---|---|---|---|

1 | 2660 | 2.64 | 10.34 | 3.24 | 38.50 | 29.50 |

2 | 2660 | 2.64 | 10.78 | 2.28 | 28.90 | 30.00 |

3 | 2369 | 2.64 | 10.37 | 2.05 | 24.80 | 23.30 |

4 | 2561 | 2.64 | 10.62 | 2.78 | 30.20 | 26.00 |

${\mathit{P}}_{\mathit{T}}{\mathbf{(}}^{\mathbf{\xb0}}\mathbf{C}\mathbf{)}$ | ${\mathit{c}}_{\mathit{cool}}$ | ${\mathit{P}}_{\mathit{T}}{\mathbf{(}}^{\mathbf{\xb0}}\mathbf{C}\mathbf{)}$ | ${\mathit{c}}_{\mathit{cool}}$ | ${\mathit{P}}_{\mathit{T}}{\mathbf{(}}^{\mathbf{\xb0}}\mathbf{C}\mathbf{)}$ | ${\mathit{c}}_{\mathit{cool}}$ | ${\mathit{P}}_{\mathit{T}}{\mathbf{(}}^{\mathbf{\xb0}}\mathbf{C}\mathbf{)}$ | ${\mathit{c}}_{\mathit{cool}}$ |
---|---|---|---|---|---|---|---|

8 | 1.000 | 12 | 0.632 | 16 | 0.347 | 20 | 0.139 |

9 | 0.897 | 13 | 0.554 | 17 | 0.288 | 22 | 0.063 |

10 | 0.804 | 14 | 0.480 | 18 | 0.233 | 24 | 0.007 |

11 | 0.716 | 15 | 0.411 | 19 | 0.184 | 26 | 0.000 |

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**MDPI and ACS Style**

Rita, M.; Fairbairn, E.; Ribeiro, F.; Andrade, H.; Barbosa, H.
Optimization of Mass Concrete Construction Using a Twofold Parallel Genetic Algorithm. *Appl. Sci.* **2018**, *8*, 399.
https://doi.org/10.3390/app8030399

**AMA Style**

Rita M, Fairbairn E, Ribeiro F, Andrade H, Barbosa H.
Optimization of Mass Concrete Construction Using a Twofold Parallel Genetic Algorithm. *Applied Sciences*. 2018; 8(3):399.
https://doi.org/10.3390/app8030399

**Chicago/Turabian Style**

Rita, Mariane, Eduardo Fairbairn, Fernando Ribeiro, Henrique Andrade, and Helio Barbosa.
2018. "Optimization of Mass Concrete Construction Using a Twofold Parallel Genetic Algorithm" *Applied Sciences* 8, no. 3: 399.
https://doi.org/10.3390/app8030399