# Rebar Shape Time-Evolution During a Reinforced Concrete Corrosion Test: An Electrochemical Model

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{−}) content of 2% relative to cement weight [24]. One 12-mm diameter steel bar was embedded in each sample with a 10-mm mortar cover depth. The ends of the steel bar were protected with vinyl electric tape, which left an exposed steel area of 120 cm

^{2}(surface of contact steel-mortar). Specimens were cured during seven days in a humid chamber (20 °C and 95% relative humidity). Before starting the forced corrosion test, the spontaneous corrosion rate of the steel bar was measured through the linear polarization technique, using the portable corrosion rate meter Gecor8 (Geocisa, Madrid, Spain).

## 3. Rebar Shape Model

^{2}. The measured open circuit corrosion rate, due to the presence of Cl

^{−}ions, showed values in the range 0.7 μA/cm

^{2}to 3 μA/cm

^{2}. Since this is much lower than the impressed current during the test, it seems suitable neglecting spontaneous corrosion contribution to metal loss in the model. Moreover, theoretical metal loss (evaluated using Faraday’s law for a 100 μA/cm

^{2}current density) is consistent with experimentally observed metal loss. Experimental to the theoretical metal loss ratio mean value was found to be 1.05, with a standard deviation of 0.19 (three samples) [27].

#### 3.1. Initial Current Density

#### 3.2. Current Density Time-Evolution

#### 3.3. Rebar Shape Time-Evolution

## 4. Results

^{2}and 46.14 μA/cm

^{2}. It is worth noting that, due to the reinforced mortar specimen geometry, cracks appear first on the side where the current density is lower.

## 5. Conclusions

- Rebar-shape time-evolution during a forced corrosion test can be estimated.
- The side of the rebar nearest to the cathode is the most affected by corrosion, suffering the highest current density, highest metal radius reduction, and highest volume increase due to corrosion product creation.
- When the first cracks appear, the rebar radius increases on the side nearest the mortar surface, which is about 6 m.
- Dependence of the expanded rebar radius along the rebar perimeter is approximately sinusoidal with a perimeter angle if corrosion time is not very long.
- The estimated rebar shape time-evolution could be used as input for a mechanical mortar cracking model in order to estimate crack evolution during the forced corrosion test.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Section of the mortar sample in the corrosion test (

**left**) and boundary conditions applied (

**right**, see text for details).

**Figure 2.**Initial mesh (

**left**) and a detail of the mesh after one year of corrosion (

**right**). The blue line shows the initial rebar shape.

**Figure 3.**Current streamlines (20 of them are shown) initially (

**left**) and after one year of corrosion (

**right**). Dashed line shows the oxide layer.

**Figure 6.**Difference of oxide radius with respect to the initial radius versus $\mathrm{cos}\theta $ after four days and 23 days of corrosion.

Material | Amount (g) |
---|---|

Cement (CEM I 52.5 R SR (3)) [25] | 450 |

Standard siliceous sand | 1350 |

Deionized water | 225 (w/c = 0.5) |

NaCl | 14.8 (2% relative to cement weight) |

Parameters | ||

${L}_{x}=4\text{\hspace{0.17em}}\mathrm{cm}$ | ${L}_{y}=8\text{\hspace{0.17em}}\mathrm{cm}$ | $\Delta t=0.5\text{\hspace{0.17em}}\mathrm{day}$ |

$D=1.2\text{\hspace{0.17em}}\mathrm{cm}$ | $c=1\text{\hspace{0.17em}}\mathrm{cm}$ | $\Delta r=1\text{\hspace{0.17em}}\mathrm{mm}$ |

${n}_{x}=30$ | ${n}_{y}=60$ | ${n}_{b}=50$ |

Obtained mesh | ||

Mesh | Nodes | Elements |

Initial | 1855 | 3490 |

After 1 year | 1868 | 3514 |

**Table 3.**Difference of radii for the metal and for the layer of oxides calculated at several corrosion times.

$\mathit{\Delta}{\mathit{r}}_{\mathit{m}}\text{\hspace{0.17em}}\left(\mathsf{\mu}\mathbf{m}\right)$ | $\mathit{\Delta}{\mathit{r}}_{\mathit{o}\mathit{x}}\text{\hspace{0.17em}}\left(\mathsf{\mu}\mathbf{m}\right)$ | |||
---|---|---|---|---|

Top | Bottom | Top | Bottom | |

4 days | - | −19.6 | 5.9 | 19.6 |

23 days | −34.7 | −113.2 | 33.9 | 111.1 |

1 year | −666.9 | −1932.1 | 599.8 | 1446.6 |

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**MDPI and ACS Style**

de Vera, G.; Miró, M.; Segovia, E.G.; Poveda, P.; Climent, M.Á.
Rebar Shape Time-Evolution During a Reinforced Concrete Corrosion Test: An Electrochemical Model. *Appl. Sci.* **2019**, *9*, 3061.
https://doi.org/10.3390/app9153061

**AMA Style**

de Vera G, Miró M, Segovia EG, Poveda P, Climent MÁ.
Rebar Shape Time-Evolution During a Reinforced Concrete Corrosion Test: An Electrochemical Model. *Applied Sciences*. 2019; 9(15):3061.
https://doi.org/10.3390/app9153061

**Chicago/Turabian Style**

de Vera, Guillem, Marina Miró, Enrique Gonzalo Segovia, Pedro Poveda, and Miguel Ángel Climent.
2019. "Rebar Shape Time-Evolution During a Reinforced Concrete Corrosion Test: An Electrochemical Model" *Applied Sciences* 9, no. 15: 3061.
https://doi.org/10.3390/app9153061