# Long Short-Term Memory-Based Methodology for Predicting Carbonation Models of Reinforced Concrete Slab Bridges: Case Study in South Korea

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## Abstract

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## Featured Application

**The proposed methodology creates LSTM-based carbonation models using the data from existing bridges. The proposed methodology and results can help bridge managers to conduct preventive maintenance.**

## Abstract

## 1. Introduction

_{2}concentration (278 to 400 ppm during the industrial period [4]) may accelerate the carbonation of cement and concrete [5,6]. Owing to these limitations, establishing a mathematical calculation model to accurately reflect the various factors of complex carbonation is difficult. Therefore, a novel approach that differs from the existing theories is required.

## 2. Literature Review

#### 2.1. Concrete Carbonation Model

_{3}) is produced by the reaction of calcium hydroxide Ca(OH)

_{2}and C-S-H in a hydrated cement paste. This action gradually lowers the concrete pH from 12 to 9. Although carbonation can increase the strength of concrete, the properties of steel change when carbonation reaches the steel reinforcement. A corroded rebar has a larger volume than steel, which leads to concrete damage, spalling, and cracking [24]. Despite maintaining a certain covering depth of rebars to prevent this deterioration, carbonation continues over time. Several studies have focused on short-term carbonation (within a year) to predict carbonation rates. Until 1980, the carbonation depth was predicted using a linear regression method based on compounding variables, such as material ratio, binder type, and certain environmental variables [25,26]. Subsequent studies have proposed mathematical and analytical models for predicting the carbonation depth of concrete [27]. Most studies are based on the theory of diffusion based on Fick’s second law, which states that the depth of concrete carbonization is proportional to the square root of time, as indicated in Equation (1) [28,29,30].

_{2}, considering reactivity as a parameter. This coefficient is primarily influenced by various factors, such as cement or binder, water–binder ratio, curing time, CO

_{2}concentration, and relative humidity. Because these equations are based on laboratory conditions, they exhibit a relatively high error in field conditions owing to changes in the influencing factors. Sisomphon and Franke [33], Dhir et al. [34], and Roy et al. [35] proposed equations to modify the exponent of t according to environmental changes. Furthermore, a fib model [36,37] has previously been applied to bridge abutment and pier carbonation data using an equation based on a robust prediction model.

#### 2.2. LSTM

#### 2.3. Padding and Masking Methods

#### 2.4. Evaluation Index of the Carbonation Models

## 3. Data Collection for the Case Study of Natural Carbonation

#### 3.1. Data Description of Inspection Reports

#### 3.2. Data Description of Environmental Conditions

## 4. LSTM-Based Methodology for Generating the Carbonation Model

## 5. Experimental Results

#### 5.1. Experimental Results of the Case Study

#### 5.2. Comparison of the Proposed Methodology with Other Analysis Methods

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**History of environmental conditions according to regions: (

**a**) average temperature; (

**b**) difference in daily temperature; (

**c**) relative humidity; (

**d**) carbon dioxide concentration; (

**e**) precipitation; and (

**f**) number of snowy days.

**Figure 8.**Carbonation prediction results of the LSTM model for the (

**a**) training and (

**b**) validation datasets.

Region | Number of Reports | Characteristics | $\mathbf{Area}\left(\mathrm{k}{\mathrm{m}}^{2}\right)$ |
---|---|---|---|

Region A | 137 | High-densely downtown area | 600 |

Region B | 22 | Low-density coastal area | 1850 |

Region C | 166 | Low-density island | 10,550 |

Classification | Factors | Average | Min | Max |
---|---|---|---|---|

Carbonation-related factors | Service life | 24.79 | 5 | 47 |

Year of construction | 1989.65 | 1969 | 2010 | |

Concrete strength | 23.42 | 18 | 35 | |

Indirect factors | Length | 83.19 | 5.2 | 261 |

Maximum span length | 17.70 | 5 | 55 | |

Width | 18.87 | 4 | 61.48 | |

Height | 6.67 | 2 | 29.5 | |

Loading condition for design | 22.08 | 13.5 | 24 | |

Element position (superstructure and substructure) | - | 0 (superstructure) | 1 (substructure) | |

Carbonation | Carbonation depth | 10.510 | 2 | 40 |

Classification | Factors | Region | Average | Min | Max |
---|---|---|---|---|---|

Temperature (°C) | Average temperature | A | 12.1 | 9.6 | 13.8 |

B | 13.6 | 12.2 | 14.8 | ||

C | 15.5 | 13.9 | 17.5 | ||

Daily temperature difference | A | 9.0 | 7.8 | 11.4 | |

B | 17.5 | 12.8 | 20.5 | ||

C | 3.4 | 2.9 | 4 | ||

Humidity | Relative humidity | A | 66.4 | 56.6 | 73.6 |

B | 66.8 | 61 | 72 | ||

C | 71.7 | 61.8 | 79.8 | ||

Carbon dioxide | Carbon dioxide concentration | A | 327.5 | 233.5 | 421.4 |

B | |||||

C | |||||

Precipitation | Precipitation | A | 1344.9 | 623.5 | 2355.5 |

B | 1431.7 | 819.3 | 2195.5 | ||

C | 1465.9 | 773.3 | 2526 | ||

Chloride penetration | Number of snowy days | A | 27.1 | 3 | 50 |

B | 6.6 | 0 | 21 | ||

C | 22.0 | 5 | 44 |

Number | Layer Name | Hidden Unit | Activation Function | Number of Parameters |
---|---|---|---|---|

1 | LSTM | 30 | tanh | 5400 |

- | Dropout | - | - | |

2 | LSTM | 30 | ReLU | 7320 |

- | Dropout | - | - | |

3 | LSTM | 30 | tanh | 7320 |

- | Dropout | - | - | |

4 | Dense | 1 | Linear | 31 |

Performance Indicator | Value |
---|---|

Training dataset ${R}^{2}$ | 0.638 |

Training dataset RMSE | 4.572 |

Validation dataset ${R}^{2}$ | 0.504 |

Validation dataset RMSE | 5.057 |

Region | Methodology | ${\mathit{R}}^{2}$ | RMSE |
---|---|---|---|

A | Proposed model | 0.426 | 4.970 |

Fick’s second law equation | 0.035 | 6.411 | |

B | Proposed model | 0.542 | 5.556 |

Fick’s second law equation | 0.129 | 7.377 | |

C | Proposed model | 0.677 | 5.132 |

Fick’s second law equation | 0.016 | 8.793 |

Regression Analysis Method | Validation Dataset | ||
---|---|---|---|

${\mathit{R}}^{2}$ | RMSE | ||

Linear regression | Linear | 0.1322 | 7.260 |

Interaction linear | 0.2203 | 6.898 | |

Robust linear | 0.1302 | 7.373 | |

Stepwise linear | 0.2102 | 6.928 | |

Tree | Complex tree | 0.3877 | 6.157 |

Medium tree | 0.3367 | 6.363 | |

Simple tree | 0.2161 | 6.932 | |

Support vector machine | Linear | 0.1259 | 7.537 |

Quadratic | 0.2457 | 6.868 | |

Cubic | 0.2229 | 7.182 | |

Fine Gaussian | 0.3756 | 6.220 | |

Gaussian process regression | Squared exponential | 0.4220 | 5.964 |

Matern 5/2 | 0.4235 | 5.955 | |

Rational quadratic | 0.4310 | 5.910 |

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**MDPI and ACS Style**

Kwon, T.H.; Kim, J.; Park, K.-T.; Jung, K.-S.
Long Short-Term Memory-Based Methodology for Predicting Carbonation Models of Reinforced Concrete Slab Bridges: Case Study in South Korea. *Appl. Sci.* **2022**, *12*, 12470.
https://doi.org/10.3390/app122312470

**AMA Style**

Kwon TH, Kim J, Park K-T, Jung K-S.
Long Short-Term Memory-Based Methodology for Predicting Carbonation Models of Reinforced Concrete Slab Bridges: Case Study in South Korea. *Applied Sciences*. 2022; 12(23):12470.
https://doi.org/10.3390/app122312470

**Chicago/Turabian Style**

Kwon, Tae Ho, Jaehwan Kim, Ki-Tae Park, and Kyu-San Jung.
2022. "Long Short-Term Memory-Based Methodology for Predicting Carbonation Models of Reinforced Concrete Slab Bridges: Case Study in South Korea" *Applied Sciences* 12, no. 23: 12470.
https://doi.org/10.3390/app122312470