# Effect of Crack on Durability of RC Material under the Chloride Aggressive Environment

^{*}

## Abstract

**:**

## 1. Introduction

^{2+}+ 2e

^{−}) at the anodic area of rebar. The electrons given by anodic area are consumed at the cathodic area (O

_{2}+ 2H

_{2}O + 4e

^{−}→ 4OH

^{−}). Pore solution as a conducting medium for the transportation of electrons and ions ensure the corrosion process to proceed [20]. The electrochemical nature of corrosion means that electrochemical techniques can be used to monitor the corrosion behavior such as corrosion rate or corrosion current density of rebar in concrete. The commonly used electrochemical techniques include liner polarization (LP), Tafel potentiodynamic polarization (TPP) and electrochemical impedance spectroscopy (EIS) measurements [21]. These techniques are widely used in the studies of carbon steel and alloy steel corrosion [22]. There are a large volume of published researches describing the corrosion behavior of rebar by immersing them into chloride solution [23] or cement extract solution [24,25]. Meanwhile, some researches focus on the corrosion behavior of rebar in real concrete material. Andrade et al. [26] analyzed influence of environmental factors and cement chemistry on corrosion behavior of rebars in concrete by using EIS measurement, and they indicated that redox activity caused by harmful ions in the rebar’s oxides layer greatly influences the electrochemical behavior of rebars in the passivity potential domain. In addition, Andrade et al. [27] indicated that different geometrical dispositions of the electrodes used in EIS measurement may affect the test results much. Wang et al. [21] analyzed corrosion rate of rebar in concrete under cyclic freeze-thaw and chloride salt action using LP and TPP measurements. They illustrated that TPP measurement is rapid and easy to operate, read corrosion current directly and provides sufficiently accurate results. Gerengi et al. [28] used EIS measurements to investigate corrosion behavior of rebar in reinforced concrete exposed to sulphuric acid, and they claimed that EIS measurement is one of the most widely used techniques in recent years. Andrade and Alonso [29] applied a non-destructive electrochemical test method for the estimation in large size concrete structures of the instantaneous corrosion current density and discussed the accuracy and applicability of this measurement used in real RC material. In summary, most of the literatures applied one of the electrochemical measurements. However, combining multiple electrochemical measurements may show a more accurate way to undertake the study on rebar corrosion.

_{corr}) of rebar was treated as the index for estimating the effect of crack on durability of RC material. Firstly, i

_{corr}values of rebar were tested by TPP, LP and EIS measurements. Subsequently, a more reasonable electrochemical testing method was recommended for rebar in RC material. Finally, the effect of crack width, number and spacing on durability of RC material was analyzed by statistical analysis methods.

## 2. Materials and Methods

#### 2.1. Materials and Mixture

#### 2.2. Specimen Preparation

#### 2.3. Experimental Methods

#### 2.3.1. Scheme Design

#### 2.3.2. Vacuum-Saturated Treatment

#### 2.3.3. Accelerated Chloride Penetration Experiment

^{3}. Cathode cell was filled with 3.5 wt % NaCl solution, and anode cell was filled with 0.3 mol/L NaOH solution. Two stainless steel-based plates as cathode electrode and anode electrode were placed into these two cells. The cracked surface of specimen was placed into the cathode cell, and the other side was placed into the anode cell. Then, these two cells were connected to a DC regulated power supply, and the applied voltage was 20.0 V. This designed accelerated chloride penetration system was electrified for 96 h.

#### 2.3.4. Corrosion Density Test for Bar Based on Electrochemical Measurements

_{corr}) is used as the index to evaluate the corrosion behavior of rebar.

^{2}, a saturated calomel electrode (SCE) with potassium chloride salt bridge placed in a Luggin capillary was used as the referenced electrode (RE) and a stainless steel-based plate with 2 mm × 100 mm × 150 mm was used as the counter electrode (CE).

_{corr}is the corrosion density (μA/cm

^{2}); B is the Stern-Geary coefficient (mV/Decade); R

_{p}is polarization resistance (Ω·cm

^{2}). The value of B can be calculated from TPP measurement or estimated to fall within the range from 25 mV to 52 mV. Song [33] demonstrated the estimated range value of B is applicable only in a uniform corrosion system at its corrosion potential, whereas the RC structure may be subjected to a non-uniform corrosion. The typical value (25 mV~52 mV) of B is not acceptable in a RC corrosion system. Therefore, the value of B should be calculated from TPP curves more accurately. Meanwhile, R

_{p}can be obtained from LP and EIS measurements. The details of these three measurements are as follows.

^{2}) and polarization potential E (V) under potentiodynamic polarization of rebar always conform to the Butler–Volmer equation:

_{corr}is the corrosion potential (V vs. SCE), respectively. b

_{a}and b

_{c}are the anodic Tafel slope and cathodic Tafel slope, respectively (mV/Decade). Values of these electrochemical parameters can be obtained by a curve-fitting approach named Tafel extrapolation method. Schematic illustration parameters in TPP curve are shown in Figure 5.

_{a}and b

_{c}can be calculated by

_{p}is defined as the slope of potential to current density, can be obtained as follows:

_{p}

_{1}), concrete resistance (R

_{p}

_{2}), polarization resistance of rebar (R

_{p}

_{3}), external concrete capacitance (CPE

_{1}) and double layer capacitance on the surface of rebar (CPE

_{2}).

^{2}) of this equivalent circuit is given by

_{n}and p

_{n}are parameters of CPE (μF·cm

^{2}); ω is the frequency of applied AC (Hz); j = $\sqrt{-1}$. The obtained impedance data could be analyzed by Z view program to fit with the immittance equation of this equivalent circuit.

#### 2.4. Statistical Analysis Methods

_{corr}of rebar, One-way analysis of variance (ANOVA) combined with Turkey’s honest significant difference (Turkey’s HSD) test was performed to analyze the effect of crack on rebar corrosion and determine the most significant factor that influences durability of RC material. One-way ANOVA was used in this study to determine whether crack width, number or spacing is the most significant factor, and Turkey’s HSD test was performed for further judging the accuracy of the One-way ANOVA results. The details of these two methods are as follows:

#### 2.4.1. One-Way ANOVA

_{T}can be calculated by

_{ij}is the jth experimental result of level i. N is the number of all experimental results, which is equal to m × n.

_{i}can be calculated by

_{e}can be obtained by

_{i}and MS

_{e}are the estimate of variance for level i and error, respectively. ${d}_{{f}_{i}}$ and ${d}_{{f}_{e}}$ are corresponding degrees of freedom, which can be obtained by

#### 2.4.2. Turkey’s HSD Test

_{α}. If the range value of means is larger than HSD

_{α}, the two levels are said to have significant effects on rebar corrosion.

## 3. Results and Discussion

#### 3.1. Recommendation of Reasonable Electrochemical Test Method

_{corr}values of sample B2 calculated from 3 measurements are analyzed to illustrate the reasonable electrochemical test method for rebar in the RC corrosion system.

_{a}), cathodic Tafel slopes (b

_{c}), Stern-Geary coefficient (B), corrosion current density (i

_{corr}) and corrosion potential (E

_{corr}vs. SCE) obtained from TPP curves are listed in Table 3.

_{corr}increases and E

_{corr}(vs. SCE) decreases under the action of chloride penetration. Meanwhile, both b

_{a}and b

_{c}increase, which illustrates the anodic and cathodic reactions are all accelerated and affected by the environmental loading.

_{p}is calculated from line polarization curves by Equation (4). The calculated R

_{p}and i

_{corr}from LP measurements are listed in Table 4.

_{p}is reduced while i

_{corr}increases under the action of chloride penetration, which infers that rebar is continuously corroded.

_{corr}is calculated by Equation (1), where B is obtained from TPP curves, and R

_{p}is equal to R

_{p}

_{3}. From Table 5, it can be concluded that the impedance spectra of rebar in sample B2 obtained from three continuous tests is reproducible. Besides, both R

_{p}

_{2}and R

_{p}

_{3}decrease after the chloride penetration, which indicates that material properties of concrete were degraded and the rebar was corroded gradually under the process of chloride penetration.

_{p}in TPP and LP measurements contain not only the resistance of rebar but also the resistance of concrete in the test conductive circuit, while R

_{p}from EIS measurements is exactly the resistance of rebar. Thus, R

_{p}from EIS measurements is smaller than those from TPP and LP measurements. According to Equation (1), i

_{corr}calculated from EIS measurements is greater than the others. Inductively, the reasonable way to calculate i

_{corr}of rebar is EIS measurement combined with TPP measurement, namely, R

_{p}and B should be calculated by EIS measurement and TPP measurement. After that, i

_{corr}can be calculated by Stern-Geary equation. In this way, the corrosion behavior of rebar can be judged more accurately compared with only a single measurement.

#### 3.2. The Effect of Crack on Corrosion Behavior of Rebar

_{corr}of rebar in each specimen could be obtained by the same test method of B2 discussed above. The variation of corrosion current densities is calculated by

_{corr}, the nth corrosion current density and initial corrosion current density, respectively. The results are listed in Table 6. The average value for 3 variations of i

_{corr}and corresponding standard deviations are also calculated. The results can be used to analyze effects of crack width, number and spacing on corrosion behavior of rebar under the aggressive environment. Comparative evaluations were conducted based on One-way ANOVA and Turkey’s HSD test.

_{0.01}(3,8), which means the probability is 99% that crack width and crack number present a significant influence of rebar corrosion. Meanwhile, F-value of crack number is larger than that of crack width, which means the influence of crack number is larger than crack width. Besides, F-value of crack spacing is between F

_{0.1}(1,4) and F

_{0.05}(1,4), which means that the probability is 90% that crack spacing is the significant effect on rebar corrosion.

_{0.05}–K

_{0}etc.) in crack width factor is larger than HSD

_{0.01}, which means the influence between each two levels is significant at 0.01 level. It is also proved that crack width has a statistically significant influence on rebar corrosion.

_{1}–K

_{0}etc.) in crack number factor is larger than HSD

_{0.01}, which means the influence between each two levels is significant at 0.01 level. It is also proved that crack number has a statistically significant influence on rebar corrosion.

## 4. Conclusions

- (1)
- Due to the EIS excluding the polarization resistance (R
_{p}) error caused by concrete and Stern-Geary coefficient (B) from TPP reflecting the non-uniform corrosion of rebar in RC material, a more accurate electrochemical test method combining EIS with TPP measurements was recommended for rebar corrosion behavior in RC material. - (2)
- The influences of crack parameters (i.e., crack width, number and spacing) on durability of RC material were analyzed based on One-way ANOVA and Turkey’s HSD test. Results revealed that crack number presents the most significant effect, while crack spacing possesses the least one. As for wondering that if the influence on rebar corrosion caused by total crack width of multiple cracks is equal to that caused by an individual crack width, this also has become the topic which the authors further deliberated from now on.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Specimen dimension and rebar arrangement: (

**a**) Front view of the sample; (

**b**) Stereoscopic view of the sample.

**Figure 5.**Schematic illustration of the Tafel potentiodynamic polarization (TPP) curve with Tafel electrode slopes.

Materials | Nominal Proportions (kg/m^{3}) |
---|---|

Cement | 433 |

Water | 195 |

Fine aggregate | 567 |

Coarse aggregate | 1205 |

Symbol | Crack Width (mm) | Crack Number | Crack Spacing (mm) | Sketch of Specimen |
---|---|---|---|---|

N | 0 | 0 | - | |

A1 | 0.05 | 1 | - | |

A2 | 0.1 | 1 | - | |

A3 | 0.2 | 1 | - | |

B1 | 0.1 | 2 | 15 | |

B2 | 0.1 | 2 | 25 | |

C1 | 0.1 | 3 | 15 | |

C2 | 0.1 | 3 | 25 |

b_{a} (mV/Decade) | b_{c} (mV/Decade) | B (mV/Decade) | i_{corr} (μA/cm^{2}) | E_{corr} (V) | |
---|---|---|---|---|---|

Initial | 382.11 | 160.64 | 49.17 | 1.32 | −0.38 |

Final | 583.29 | 282.93 | 82.72 | 10.55 | −0.73 |

B (mV/Decade) | R_{p} (Ω·cm^{2}) | i_{corr} (μA/cm^{2}) | |
---|---|---|---|

Initial | 49.17 | 34,384 | 1.43 |

Final | 82.72 | 7673 | 10.78 |

**Table 5.**Fitting parameters from electrochemical impedance spectroscopy (EIS) of rebar in sample B2.

R_{p}_{1}(Ω·cm ^{2}) | CPE_{1}-T(μF·cm ^{2}) | CPE_{1}-P(μF·cm ^{2}) | R_{p}_{2}(Ω·cm ^{2}) | CPE_{2}-T(μF·cm ^{2}) | CPE_{2}-P(μF·cm ^{2}) | R_{p}_{3}(Ω·cm ^{2}) | i_{corr}(μA/cm ^{2}) | |
---|---|---|---|---|---|---|---|---|

Initial | 132.5 | 3.52 × 10^{−5} | 0.76 | 2720 | 2.40 × 10^{−4} | 0.69 | 30,077 | 1.63 |

Final 1 | 154.2 | 9.07 × 10^{−5} | 0.62 | 2256 | 2.25 × 10^{−4} | 0.68 | 7540 | 10.97 |

Final 2 | 156.1 | 8.99 × 10^{−5} | 0.62 | 2197 | 2.35 × 10^{−4} | 0.64 | 7609 | 10.87 |

Final 3 | 154.6 | 8.54 × 10^{−5} | 0.62 | 2094 | 2.21 × 10^{−4} | 0.62 | 7554 | 10.95 |

Symbol | Crack Width (mm) | Crack Number | Crack Spacing (mm) | ${\mathit{i}}_{\mathit{c}\mathit{o}\mathit{r}\mathit{r}}^{1}$ (μA/cm ^{2}) | ${\mathit{i}}_{\mathit{c}\mathit{o}\mathit{r}\mathit{r}}^{2}$ (μA/cm ^{2}) | ${\mathit{i}}_{\mathit{c}\mathit{o}\mathit{r}\mathit{r}}^{3}$ (μA/cm ^{2}) | Average Value (μA/cm ^{2}) | Standard Deviation (μA/cm ^{2}) |
---|---|---|---|---|---|---|---|---|

N | 0 | 0 | - | 4.00 | 3.88 | 3.63 | 3.84 | 0.19 |

A1 | 0.05 | 1 | - | 7.81 | 7.76 | 7.68 | 7.75 | 0.07 |

A2 | 0.1 | 1 | - | 8.06 | 8.12 | 8.04 | 8.07 | 0.04 |

A3 | 0.2 | 1 | - | 8.92 | 8.86 | 8.88 | 8.89 | 0.03 |

B1 | 0.1 | 2 | 15 | 9.48 | 9.36 | 9.44 | 9.43 | 0.06 |

B2 | 0.1 | 2 | 25 | 9.24 | 9.32 | 9.34 | 9.30 | 0.05 |

C1 | 0.1 | 3 | 15 | 12.86 | 12.75 | 12.78 | 12.80 | 0.06 |

C2 | 0.1 | 3 | 25 | 12.44 | 12.54 | 12.45 | 12.48 | 0.06 |

Source of Variance | Square of Deviance | Degree of Freedom | Estimate of Variance | F-Value | F_{0.01} (3,8) | Significance |
---|---|---|---|---|---|---|

Crack width | 45.618 | 3 | 15.206 | 1427.80 | 7.59 | ** |

Error | 0.085 | 8 | 0.011 | |||

Total | 45.703 |

Source of Variance | Square of Deviance | Degree of Freedom | Estimate of Variance | F-Value | F_{0.01} (3,8) | Significance |
---|---|---|---|---|---|---|

Crack number | 123.733 | 3 | 41.244 | 3721.29 | 7.59 | ** |

Error | 0.089 | 8 | 0.011 | |||

Total | 123.822 |

Source of Variance | Square of Deviance | Degree of Freedom | Estimate of Variance | F-Value | F_{0.05} (1,4) | F_{0.1} (1,4) | Significance |
---|---|---|---|---|---|---|---|

Crack spacing | 0.024 | 1 | 0.024 | 7.367 | 7.71 | 4.54 | * |

Error | 0.013 | 4 | 0.003 | ||||

Total | 0.037 |

Source of Range Value | Range Value | q_{0.05} (4,8) | q_{0.01} (4,8) | MS_{e} | HSD_{0.05} | HSD_{0.01} | Significance |
---|---|---|---|---|---|---|---|

K_{0.05}–K_{0} | 3.91 | 7.35 | 11.5 | 0.011 | 0.445 | 0.70 | ** |

K_{0.1}–K_{0.05} | 0.32 | - | |||||

K_{0.2}–K_{0.1} | 0.82 | ** | |||||

K_{0.1}–K_{0} | 4.23 | ** | |||||

K_{0.2}–K_{0} | 5.05 | ** | |||||

K_{0.2}–K_{0.05} | 1.14 | ** |

Source of Range Value | Range Value | q_{0.05} (4,8) | q_{0.01} (4,8) | MS_{e} | HSD_{0.05} | HSD_{0.01} | Significance |
---|---|---|---|---|---|---|---|

K_{1}–K_{0} | 4.23 | 7.35 | 11.5 | 0.011 | 0.445 | 0.70 | ** |

K_{2}–K_{1} | 1.36 | ** | |||||

K_{3}–K_{2} | 3.37 | ** | |||||

K_{2}–K_{0} | 5.59 | ** | |||||

K_{3}–K_{0} | 8.96 | ** | |||||

K_{3}–K_{1} | 4.73 | ** |

Source of Range Value | Range Value | q_{0.05} (2,4) | q_{0.01} (2,4) | MS_{e} | HSD_{0.05} | HSD_{0.01} | Significance |
---|---|---|---|---|---|---|---|

K_{15}–K_{25} | 0.13 | 9.8 | 22.3 | 0.003 | 0.31 | 0.70 | - |

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## Share and Cite

**MDPI and ACS Style**

Cheng, Y.; Zhang, Y.; Tan, G.; Jiao, Y. Effect of Crack on Durability of RC Material under the Chloride Aggressive Environment. *Sustainability* **2018**, *10*, 430.
https://doi.org/10.3390/su10020430

**AMA Style**

Cheng Y, Zhang Y, Tan G, Jiao Y. Effect of Crack on Durability of RC Material under the Chloride Aggressive Environment. *Sustainability*. 2018; 10(2):430.
https://doi.org/10.3390/su10020430

**Chicago/Turabian Style**

Cheng, Yongchun, Yuwei Zhang, Guojin Tan, and Yubo Jiao. 2018. "Effect of Crack on Durability of RC Material under the Chloride Aggressive Environment" *Sustainability* 10, no. 2: 430.
https://doi.org/10.3390/su10020430