# Orthogonal Experiments and Neural Networks Analysis of Concrete Performance

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## Abstract

**:**

## 1. Introduction

## 2. Design of Experiments for Concrete Mixture

## 3. Introduction to Orthogonal Experimental Design

^{4})) was selected to optimize the concrete mix design, the specific distribution of the orthogonal test, as shown in Table 2.

## 4. About Neural Networks

## 5. Response Surfaces of Strength

- The water/binder ratio (w/b) is 0.5.
- The fly ash/binder ratio (fa/b) refers to the content of fly ash calculated by the weight of the binder, with a variation range of 10–30%.
- The age of concrete is different on the 3rd and 28th days. All other raw materials or their proportions remain unchanged.

#### 5.1. Effects of fa/b

#### 5.2. Effects of NaOH

#### 5.3. Effects of Age

#### 5.4. Interactions of fa/b and NaOH

- The effect of low and high content of fly ash replacement on the strength ratio had optimum strength and was roughly the same at 5% or 6% of NaOH. As shown in Figure 1 and Figure 2, at 3 days of age, the flexural strength of concrete with 10% fly ash at 5% or 6% of NaOH was the highest, and the compressive strength was the highest at 5% of NaOH. At 28 days, the flexural strength of concrete with 10% fly ash at 5% or 6% of NaOH was the highest, and compressive strength was the highest at 5% of NaOH.
- With the increase of fly ash, the strength decreased significantly at a high content of NaOH and decreased slightly lower at a low content of NaOH. For example, with NaOH contents of 0% and 8%, the compressive strength with 30% fly ash at 28 days of age was 74 and 66%, respectively, of concrete with 10% fly ash. At 28 days, the mortar strength reached the maximum when the fly ash accounted for 10% of the mixture, and the sodium hydroxide accounted for 6%.

#### 5.5. Interactions of fa/b and Age

- In the early stage, fly ash contributed little to strength. As shown in Figure 1 and Figure 5, when the amount of NaOH was 5%, the compressive strength of concrete replaced with 10% fly ash decreased by 8% compared with that of concrete without fly ash, and the strength ratio of concrete replaced with 30% fly ash decreased by 40%.

#### 5.6. Interactions of NaOH and Age

## 6. Analysis of Mechanical Properties Based on Orthogonal Test

_{cu}and f

_{fu}. When A1 was chosen, f

_{cu}and f

_{fu}at 28 days increased by 46.6% and 14.9%, respectively, compared with A3, so A1 was chosen. According to the comparison of B1 and B7, the 3-day f

_{cu}and f

_{fu}were 10.6% and 20% higher, respectively, than B1 when B4 was selected, but 28d f

_{fu}decreased by 3.1%, so B1 was selected.

## 7. Neural Networks for Modeling Strength Behavior

^{2}= 0.99) and 1.65 MPa (R

^{2}= 0.98), respectively. The network was used to predict concrete strength from training data and test data, as shown in Figure 9 and Figure 10, respectively. By comparing Figure 9 and Figure 10, it can be seen that for the experimental data within the concrete strength range, the model obtained by the neural network could predict the experimental results more accurately.

## 8. Conclusions

- On the basis of laboratory tests, the concrete strength analysis is conducted to test the influence of various variables and their interaction on strength. This information can be used to elicit some interesting findings about the role and interaction of factors.
- At the same NaOH and the same age, the strength ratio (the strength ratio of concrete with fly ash and concrete without (pure cement concrete)) decreases significantly with the increase of fly ash, and it decreases significantly with age. Strength is the highest roughly when the NaOH content is 6% or 5%.
- The higher the fly ash content, the lower the overall strength ratio of the mixture, the greater the early age strength reduction, and the same optimal amount of NaOH.
- When high fly ash is substituted, the strength ratio is higher than others at 5% or 6% NaOH. However, under the condition of low fly ash content, in the concrete mixture with a certain w/b content, the strength ratio reduction caused by NaOH dosage for cement is basically the same as that caused by high fly ash concrete.
- As the age decreases, the strength ratio decreases significantly, and the strength ratio decreases more when the fly ash replacement rate is high and the content of NaOH is constant.
- For concrete compressive strength, an orthogonal experimental design can analyze the primary and secondary factors and the best combination of them (cement, fly ash, NaOH, standard, water, etc.). The optimal combination of 3-day intensity was A1B4, and the optimal combination of flexural strength at 28 days was A1B5. The optimal combination of 28 days compressive strength was A1B5 or A1B1. The OED can effectively determine the importance of each factor.
- Based on the mixture data obtained from the mix design test results and orthogonal tests, using the generalization ability of the neural network, a high correlation between the strength and composition of concrete can be developed. The model can effectively simulate the compressive strength behavior of concrete. Therefore, the neural network is much more economical.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Cementitious Material/g | Standard Sand/g | Mixing Water/mL |
---|---|---|

450 ± 2 | 1350 ± 5 | 225 ± 1 |

3 Days Flexural | 3 Days Compression | 28 Days Flexural | 28 Days Compression | |||||
---|---|---|---|---|---|---|---|---|

A (Fly Ash) | B (NaOH) | A (Fly Ash) | B (NaOH) | A (Fly Ash) | B (NaOH) | A (Fly Ash) | B (NaOH) | |

$\overline{)\overline{\mathrm{k}1}}$ | 5.06 | 4.23 | 22.07 | 17.9 | 8.71 | 8.43 | 45.94 | 42.3 |

$\overline{)\overline{\mathrm{k}2}}$ | 4.67 | 4.5 | 18.86 | 18.8 | 8.33 | 7.93 | 39.2 | 37.37 |

$\overline{)\overline{\mathrm{k}3}}$ | 3.89 | 4.8 | 14.1 | 19.57 | 7.59 | 8.03 | 31.34 | 38.1 |

$\overline{)\overline{\mathrm{k}4}}$ | 5.1 | 20.57 | 8.1 | 38.57 | ||||

$\overline{)\overline{\mathrm{k}5}}$ | 4.8 | 18.5 | 8.7 | 42.17 | ||||

$\overline{)\overline{\mathrm{k}6}}$ | 4.3 | 17.07 | 8.37 | 38.47 | ||||

$\overline{)\overline{\mathrm{k}7}}$ | 4.03 | 16 | 7.9 | 34.83 | ||||

R (the average poor) | 1.17 | 1.07 | 7.97 | 4.57 | 1.12 | 0.8 | 14.6 | 7.47 |

Primary and secondary factors | A > B | A > B | A > B | A > B | ||||

Optimal combination | A1B4 | A1B4 | A1B5 | A1B1 or A1B5 |

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**MDPI and ACS Style**

Liu, F.; Xu, J.; Tan, S.; Gong, A.; Li, H.
Orthogonal Experiments and Neural Networks Analysis of Concrete Performance. *Water* **2022**, *14*, 2520.
https://doi.org/10.3390/w14162520

**AMA Style**

Liu F, Xu J, Tan S, Gong A, Li H.
Orthogonal Experiments and Neural Networks Analysis of Concrete Performance. *Water*. 2022; 14(16):2520.
https://doi.org/10.3390/w14162520

**Chicago/Turabian Style**

Liu, Feipeng, Jing Xu, Shucheng Tan, Aimin Gong, and Huimei Li.
2022. "Orthogonal Experiments and Neural Networks Analysis of Concrete Performance" *Water* 14, no. 16: 2520.
https://doi.org/10.3390/w14162520