# Life Cycle Assessment of a Coastal Concrete Bridge Aided by Non-Destructive Damage Detection Methods

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Service Life and Damage Prediction Methods

_{FF}is the PSD inputs matrix at degrees of freedom (DOF). In addition, H*(ω) is expressed as the complex conjugate of a transfer function. The PSD was shown to be a second-order function of the frequency response function in Equation (2), suggesting that it was a highly nonlinear response in structural characteristics.

_{i}) refers to the time required for chloride concentrations to rise to the point where corrosion might occur on the rebars. The chloride threshold is determined by the steel qualities and, to some degree, the concrete parameters. In addition, the period t

_{p}refers to the amount of time required for corrosion to spread across an entire structural element before the part begins to fail significantly. This research used a deterministic solution based on Fick’s law according to the chlorine diffusion in the RC structure. The equation used in this study was derived from Fib Bulletin 34 [53], whereby it is assumed that the surface chloride concentration remains constant and does not vary with time. The calculation of the initiation stage of chloride diffusion (t

_{i}) may be determined using the equation provided in reference [52].

_{0}is the chloride diffusion coefficient, C

_{s}is the surface chloride content, t

_{0}is the primary time, expressed in years, and usually considered as t

_{0}= 0.0767 (equal to 28 days), and α = 0.5 is an age factor.

_{p}) commenced subsequent to the starting stage of chloride diffusion, whereby chloride ions present on the surface of the inner rebars initiated the erosion of steel reinforcements. Over a prolonged period, the process of chloride corrosion gradually diminished the stiffness and area of the cross-section of the reinforcements. The Spanish concrete design code offers the following computation for estimating this time:

_{corr}shows the chloride corrosion rate, and ϕ is the diameter of the rebar.

_{st rebar}is the percentage of reinforcement affected by chloride ions in every time (t) since propagation t

_{p}.

_{D}(ω) is the frequency response of the corroded bridge according to Equation (8), and Z(ω) refers to the impedance matrix and is the inverse transfer function. So, the damaged elements through the PSD equation can be as follows.

_{n}

_{,}M

_{n}, and C

_{n}. The observed changes in structural parameters ΔP

_{n}

^{K}, ΔP

_{n}

^{M}, and ΔP

_{n}

^{C}fall within the range of −1 to 1. According to Equation (13) and a chloride-corroded RC bridge, the sensitivity matrices for the structure’s nth parameter determine passive stiffness ratios:

_{k}

_{,}Δp

_{M}

_{,}and Δp

_{C}illustrate the differences in the structural stiffness caused by deterioration over time using the PSD method and equations for the corrosion of the reinforcement.

#### 2.2. Life Cycle Assessment

#### Environmental Impact Assessment

^{®}(Data quality guideline for the ecoinvent database version 3. St. Gallen, Switzerland) and Ecoinvent

^{®}(The ecoinvent Database is a Life Cycle Inventory (LCI) database that supports various types of sustainability assessments. Zurich, Switzerland) are the most popular databases [56]. ISO 14040 [45] and ISO 14044 [46] have standardized specifications for different systemic analysis approaches. Figure 5 demonstrates the ReCiPe [57,58] method for the midpoint and endpoint indicators.

## 3. Model Description

_{cm}equaled 40 MPa, and the modulus of elasticity Ec equaled 29 GPa.

_{0}= 10 × 10

^{−12}m²/s, and the critical chloride threshold C

_{crit}= 0.6%. The third parameter that determined the chloride advance through concrete over time was the so-called surface chloride concentration, which depended on the chloride content in contact with the concrete element. Based on the distance between the structure and the seawater, a surface chloride content of 3.34% (C

_{s,0}) was used to assess the bridge deck [52].

#### The Numerical Model Analyses

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The general diagram stages of the damage detection method for the life cycle assessment that this research proposes.

**Figure 3.**Reinforcement concrete structure’s rebar service life according to Tuutti’s model (1982) [50].

**Figure 4.**The approaches to environmental life cycle assessment [55].

**Table 1.**Durability parameters in a coastal reinforced concrete bridge [42].

Marine Exposure Classification | C_{s}(% of Concrete Weight) | V_{corr}(μm/Year) | D_{0}(×10 ^{−12} m^{2}/s) |
---|---|---|---|

Aerial (IIIa) | 0.14 | 20 | 10.0 |

Submerged (IIIb) | 0.72 | 4 | |

In tide zone (IIIc) | 0.50 | 50 |

Impact Category | Environmental Impact (Points) | |||
---|---|---|---|---|

Desk | Columns | |||

Conventional | PSD | Conventional | PSD | |

Ecosystem quality | ||||

Agricultural land occupation | 1872.4 | 268.3 | 2313.8 | 685.4 |

Climate change, ecosystems | 46,192.7 | 6620.7 | 57,082.6 | 16,909.2 |

Freshwater ecotoxicity | 5.9 | 0.8 | 7.3 | 2.1 |

Freshwater eutrophication | 23.4 | 3.3 | 29.0 | 8.5 |

Marine ecotoxicity | 129.2 | 18.5 | 159.6 | 47.2 |

Natural land transformation | 22,668.7 | 3249.0 | 28,012.8 | 8298.0 |

Terrestrial acidification | 151.4 | 21.7 | 187.1 | 55.4 |

Terrestrial ecotoxicity | 512.9 | 73.5 | 633.8 | 187.7 |

Urban land occupation | 444.1 | 63.6 | 548.8 | 162.5 |

Human health | ||||

Climate change, human health | 58,117.0 | 8329.8 | 71,818.1 | 21,274.2 |

Human toxicity | 72,315.3 | 10,364.8 | 89,363.6 | 26,471.6 |

Ionizing radiation | 60.7 | 8.7 | 75.0 | 22.2 |

Ozone depletion | 3.7 | 0.5 | 4.6 | 1.3 |

Particulate matter formation | 7975.7 | 1143.1 | 9855.9 | 2919.5 |

Photochemical oxidant formation | 206.7 | 29.6 | 255.5 | 75.6 |

Resources | ||||

Fossil depletion | 49,089.4 | 7035.9 | 60,662.3 | 17,969.6 |

Metal depletion | 8142.3 | 1167.0 | 10,061.9 | 2980.5 |

Impact Category | Difference | Impact Category | Difference |
---|---|---|---|

Ecosystem Quality | Human Health | ||

Agricultural land occupation | 3232.5 | Climate change, human health | 100,331 |

Climate change, ecosystems | 79,745.4 | Human toxicity | 124,842.5 |

Freshwater ecotoxicity | 10.3 | Ionizing radiation | 104.7 |

Freshwater eutrophication | 40.5 | Ozone depletion | 6.54 |

Marine ecotoxicity | 223 | Particulate matter formation | 13,768.9 |

Natural land transformation | 39,134.4 | Photochemical oxidant formation | 356.9 |

Terrestrial acidification | 261.4 | Resources | |

Terrestrial ecotoxicity | 885.5 | Fossil depletion | 84,746.2 |

Urban land occupation | 766.71 | Metal depletion | 14,056.6 |

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**MDPI and ACS Style**

Hadizadeh-Bazaz, M.; Navarro, I.J.; Yepes, V.
Life Cycle Assessment of a Coastal Concrete Bridge Aided by Non-Destructive Damage Detection Methods. *J. Mar. Sci. Eng.* **2023**, *11*, 1656.
https://doi.org/10.3390/jmse11091656

**AMA Style**

Hadizadeh-Bazaz M, Navarro IJ, Yepes V.
Life Cycle Assessment of a Coastal Concrete Bridge Aided by Non-Destructive Damage Detection Methods. *Journal of Marine Science and Engineering*. 2023; 11(9):1656.
https://doi.org/10.3390/jmse11091656

**Chicago/Turabian Style**

Hadizadeh-Bazaz, Mehrdad, Ignacio J. Navarro, and Víctor Yepes.
2023. "Life Cycle Assessment of a Coastal Concrete Bridge Aided by Non-Destructive Damage Detection Methods" *Journal of Marine Science and Engineering* 11, no. 9: 1656.
https://doi.org/10.3390/jmse11091656