# Experimental Investigation on Seismic Performance of Non-Uniformly Corroded RC Moment-Resisting Frames

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Program

#### 2.1. Specimen Information

_{corr}

_{,1}and A

_{corr}

_{,2}are the larger and smaller corroded average loss area of reinforcement of two sides of the cross-section, respectively; A

_{corr,all}is the total average corroded loss area of reinforcement of the member.

#### 2.2. Electrochemical Accelerated Corrosion

^{2}. Three DC power supplies were used to control the current in each specimen, and an independent DC power supply powered each member (Column A, Column B, and Beam). The longitudinal reinforcement in each member was connected in parallel. The target corrosion rate was controlled by controlling the energizing duration of each part.

#### 2.3. Test Setup, Instrumentation, and Loading Protocol

## 3. Experimental Results

#### 3.1. Damage Due to Corrosion

#### 3.2. Damage Evolution

#### 3.3. Hysteresis Behavior

#### 3.4. Stiffness Degradation

_{0}is the initial stiffness and K

_{i}is the effective stiffness of the specimen at the loading displacement amplitude ∆

_{i}, which is calculated as

_{i}is the peak load of the loading displacement amplitude ∆

_{i}within the first cycle. The stiffness of the specimen decreases rapidly in the initial stage. With the increase in loading displacement amplitude, the stiffness decreases slowly. For the corroded specimens S2, S4, and S7, the stiffness degradation increases slightly with the increase in the average corrosion ratio, but the trend is not obvious. The initial stiffness of the specimens do not change much with the increase in the average corrosion ratio. Due to corrosion damage, the cover concrete failed more easily during the loading process, which reduced the stiffness of the specimen. The stiffness degradation of specimens S3, S4, and S5 gradually increases with the increase in the non-uniform corrosion characteristic value. However, it is not noticeable when the non-uniform corrosion characteristic values are small. The stiffness degradation of S4 is more significant than that of S6, which is mainly due to the larger initial stiffness of the specimen with a larger axial compression ratio.

#### 3.5. Energy Dissipation Capacity

#### 3.6. Quantitative Evaluation of Corrosion Effect

_{S}is the coefficient of lateral load bearing capacity which is the bearing capacity of the corroded frame divided by that of uncorroded frame (specimen S1), C

_{D}is the coefficient of displacement ductility, which is the displacement ductility ratio of the corroded frame divided by that of uncorroded frame, and C

_{E}is the coefficient of energy dissipation capacity, which is the cumulative energy dissipation at ultimate displacement of the corroded frame divided by that of uncorroded frame. The comparison between the fitting expression results and the test results is shown in Figure 14. It can be found that the effect of non-uniform corrosion on the energy dissipation capacity of the RC frame is more significant. Due to the limited quantity of samples, the fitting expressions proposed in this study are only applicable to this situation, for which the average corrosion ratio is less than 15% and the non-uniform corrosion characteristics value is less than 0.8.

## 4. Conclusions

- (1)
- With the increase in the average corrosion ratio, the bearing capacity, energy dissipation capacity, and deformation capacity of the RC frame decrease, and the stiffness degradation becomes more significant. This adverse effect should be considered in the seismic design and assessment of RC structures.
- (2)
- With the increase in the non-uniform corrosion characteristic value, the unidirectional bearing capacity, energy dissipation capacity, and deformation capacity of the RC frame decrease, the stiffness degradation of the RC frame becomes more significant, the damage develops more rapidly, and the damage distribution is more concentrated.
- (3)
- In small axial compression ratio ranges, with the increase in the axial compression ratio, the bearing capacity and energy dissipation capacity of the RC frame increase, and the stiffness degradation is more significant.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Fu, C.; Fang, D.; Ye, H.; Huang, L.; Wang, J. Bond Degradation of Non-Uniformly Corroded Steel Rebars in Concrete. Eng. Struct.
**2021**, 226, 111392. [Google Scholar] [CrossRef] - Chen, E.; Berrocal, C.G.; Fernandez, I.; Löfgren, I.; Lundgren, K. Assessment of the Mechanical Behaviour of Reinforcement Bars with Localised Pitting Corrosion by Digital Image Correlation. Eng. Struct.
**2020**, 219, 110936. [Google Scholar] [CrossRef] - Chung, L.; Jay Kim, J.; Yi, S. Bond Strength Prediction for Reinforced Concrete Members with Highly Corroded Reinforcing Bars. Cem. Concr. Compos.
**2008**, 30, 603–611. [Google Scholar] [CrossRef] - Ruggieri, S.; Porco, F.; Uva, G. A Practical Approach for Estimating the Floor Deformability in Existing Rc Buildings: Evaluation of the Effects in the Structural Response and Seismic Fragility. Bull. Earthq. Eng.
**2020**, 18, 2083–2113. [Google Scholar] [CrossRef] - Ruggieri, S.; Calò, M.; Cardellicchio, A.; Uva, G. Analytical-Mechanical Based Framework for Seismic Overall Fragility Analysis of Existing Rc Buildings in Town Compartments. Bull. Earthq. Eng.
**2022**, 20, 8179–8216. [Google Scholar] [CrossRef] - Yadav, D.; Kwatra, N.; Agarwal, P. Comparative Post-Yield Performance Evaluation of Flexure Member with Corroded Reinforcement. Struct. Infrastruct. Eng.
**2021**, 17, 103–123. [Google Scholar] [CrossRef] - Huang, L.; Ye, H.; Jin, X.; Jin, N.; Xu, Z. Corrosion-Induced Shear Performance Degradation of Reinforced Concrete Beams. Constr. Build. Mater.
**2020**, 248, 118668. [Google Scholar] [CrossRef] - Firouzi, A.; Taki, A.; Mohammadzadeh, S. Time-Dependent Reliability Analysis of RC Beams Shear and Flexural Strengthened with CFRP Subjected to Harsh Environmental Deteriorations. Eng. Struct.
**2019**, 196, 109326. [Google Scholar] [CrossRef] - Ma, Y.; Che, Y.; Gong, J. Behavior of Corrosion Damaged Circular Reinforced Concrete Columns Under Cyclic Loading. Constr. Build. Mater.
**2012**, 29, 548–556. [Google Scholar] [CrossRef] - Shang, Z.; Zheng, S.; Zheng, H.; Li, Y.; Dong, J. Seismic Behavior and Damage Evolution of Corroded RC Columns Designed for Bending Failure in an Artificial Climate. Structures
**2022**, 38, 184–201. [Google Scholar] [CrossRef] - Dang, V.H.; François, R. Prediction of Ductility Factor of Corroded Reinforced Concrete Beams Exposed to Long Term Aging in Chloride Environment. Cem. Concr. Compos.
**2014**, 53, 136–147. [Google Scholar] [CrossRef] - Okada, K.; KobayashiI, K.; Miyagawa, T. Influence of Longitudinal Cracking Due to Reinforcement Corrosion on Characteristics of Reinforced Concrete Members. ACI Struct. J.
**1988**, 85, 134–140. [Google Scholar] - Torres-Acosta, A.A.; Fabela-Gallegos, M.J.; Muñoz-Noval, A.; Vázquez-Vega, D.; Hernandez-Jimenez, J.R.; Martínez-Madrid, M. Influence of Corrosion on the Structural Stiffness of Reinforced Concrete Beams. Corrosion
**2004**, 60, 862–872. [Google Scholar] [CrossRef] - Meda, A.; Mostosi, S.; Rinaldi, Z.; Riva, P. Experimental Evaluation of the Corrosion Influence on the Cyclic Behaviour of RC Columns. Eng. Struct.
**2014**, 76, 112–123. [Google Scholar] [CrossRef] - Goksu, C.; Ilki, A. Seismic Behavior of Reinforced Concrete Columns with Corroded Deformed Reinforcing Bars. ACI Struct. J.
**2016**, 113, 1053–1064. [Google Scholar] [CrossRef] - Biswas, R.K.; Iwanami, M.; Chijiwa, N.; Uno, K. Effect of Non-Uniform Rebar Corrosion on Structural Performance of RC Structures: A Numerical and Experimental Investigation. Constr. Build. Mater.
**2020**, 230, 116908. [Google Scholar] [CrossRef] - Chen, J.; Zhang, W.; Gu, X. Modeling Time-Dependent Circumferential Non-Uniform Corrosion of Steel Bars in Concrete Considering Corrosion-Induced Cracking Effects. Eng. Struct.
**2019**, 201, 109766. [Google Scholar] [CrossRef] - Su, R.K.L.; Zhang, Y. A Novel Elastic-Body-Rotation Model for Concrete Cover Spalling Caused by Non-Uniform Corrosion of Reinforcement. Constr. Build. Mater.
**2019**, 213, 549–560. [Google Scholar] [CrossRef] - Zhao, Y.; Karimi, A.R.; Wong, H.S.; Hu, B.; Buenfeld, N.R.; Jin, W. Comparison of Uniform and Non-Uniform Corrosion Induced Damage in Reinforced Concrete Based on a Gaussian Description of the Corrosion Layer. Corros. Sci.
**2011**, 53, 2803–2814. [Google Scholar] [CrossRef] [Green Version] - Zhang, M.; Song, H.; Lim, S.; Akiyama, M.; Frangopol, D.M. Reliability Estimation of Corroded RC Structures Based on Spatial Variability Using Experimental Evidence, Probabilistic Analysis and Finite Element Method. Eng. Struct.
**2019**, 192, 30–52. [Google Scholar] [CrossRef] - Zhang, M.; Nishiya, N.; Akiyama, M.; Lim, S.; Masuda, K. Effect of the Correlation of Steel Corrosion in the Transverse Direction Between Tensile Rebars on the Structural Performance of RC Beams. Constr. Build. Mater.
**2020**, 264, 120678. [Google Scholar] [CrossRef] - Ye, Z.; Zhang, W.; Gu, X. Deterioration of Shear Behavior of Corroded Reinforced Concrete Beams. Eng. Struct.
**2018**, 168, 708–720. [Google Scholar] [CrossRef] - Yuan, W.; Guo, A.; Li, H. Experimental Investigation on the Cyclic Behaviors of Corroded Coastal Bridge Piers with Transfer of Plastic Hinge Due to Non-Uniform Corrosion. Soil Dyn. Earthq. Eng.
**2017**, 102, 112–123. [Google Scholar] [CrossRef] - Li, D.; Wei, R.; Xing, F.; Sui, L.; Zhou, Y.; Wang, W. Influence of Non-Uniform Corrosion of Steel Bars on the Seismic Behavior of Reinforced Concrete Columns. Constr. Build. Mater.
**2018**, 167, 20–32. [Google Scholar] [CrossRef] - GB50011-2010; Code for Seismic Design of Buildings. Ministry of Housing and Urban-Rural Development of the People’s Republic of China: Beijing, China, 2016.
- Lund University. Contecvet—A Validated Users Manual for Assessing the Residual Service Life of Concrete Structures; Report TVBM (Intern 7000-Rapport); Lund University: Lund, Sweden, 2001. [Google Scholar]
- Liu, X.; Jiang, H.; He, L. Experimental Investigation on Seismic Performance of Corroded Reinforced Concrete Moment-resisting Frames. Eng. Struct.
**2017**, 153, 639–652. [Google Scholar] [CrossRef] - Park, R. Evaluation of Ductility of Structures and Structural Assemblages from Laboratory Testing. Bull. N. Z. Soc. Earthq. Eng.
**1989**, 22, 155–166. [Google Scholar] [CrossRef]

**Figure 8.**Distribution of corrosion expansion cracks of specimens. (unit: mm): (

**a**) specimen S3; (

**b**) specimen S7.

**Figure 10.**Lateral load–displacement hysteretic curves of specimens: (

**a**) specimen S1; (

**b**) specimen S2; (

**c**) specimen S3; (

**d**) specimen S4; (

**e**) specimen S5; (

**f**) specimen S6; (

**g**) specimen S7.

**Figure 11.**Lateral load–drift ratio skeleton curves of specimens: (

**a**) different average corrosion ratio; (

**b**) different axial compression ratio; (

**c**) different non-uniform corrosion characteristic value.

**Figure 12.**Stiffness degradation of specimens: (

**a**) different average corrosion ratio; (

**b**) different axial compression ratio; (

**c**) different non-uniform corrosion characteristic value.

**Figure 13.**Cumulative energy dissipation of specimens: (

**a**) different average corrosion ratio; (

**b**) different axial compression ratio; (

**c**) different non-uniform corrosion characteristic value.

Specimen No. | η_{T} (%) | ρ_{T} | n | η_{actual} (%) | ρ_{actual} |
---|---|---|---|---|---|

S1 | 0 | - | 0.1 | - | - |

S2 | 5 | 0.6 | 0.1 | 4.8 | 0.56 |

S3 | 10 | 0.2 | 0.1 | 6.7 | 0.18 |

S4 | 10 | 0.6 | 0.1 | 9.2 | 0.59 |

S5 | 10 | 0.8 | 0.1 | 9.4 | 0.72 |

S6 | 10 | 0.6 | 0.2 | 9.3 | 0.56 |

S7 | 15 | 0.6 | 0.1 | 12.7 | 0.61 |

_{T}is the target average corrosion ratio of the longitudinal reinforcement; ρ

_{T}is the target average non-uniform corrosion characteristic value; n is the designed axial compressive load ratio; η

_{actual}is the average actual corrosion ratio; ρ

_{actual}is the average actual non-uniform corrosion characteristic value.

Specimen No. | Loading Direction | F_{y}(kN) | ∆_{y}(mm) | F_{m}(kN) | ∆_{m}(mm) | F_{u}(kN) | ∆_{u}(mm) | μ |
---|---|---|---|---|---|---|---|---|

S1 | Positive | 105.3 | 23.8 | 119.6 | 42.9 | 101.6 | 73.0 | 4.04 |

Negative | 95.6 | 13.2 | 121.9 | 57.1 | 103.6 | 76.4 | ||

S2 | Positive | 92.8 | 19.2 | 109.9 | 36.5 | 92.5 | 69.1 | 3.98 |

Negative | 64.7 | 12.4 | 108.8 | 47.0 | 93.4 | 56.5 | ||

S3 | Positive | 102.2 | 22.0 | 118.4 | 41.0 | 100.6 | 62.0 | 3.77 |

Negative | 68.2 | 13.0 | 105.5 | 46.6 | 89.6 | 70.1 | ||

S4 | Positive | 95.2 | 21.2 | 110.1 | 40.5 | 93.6 | 57.2 | 3.69 |

Negative | 56.9 | 12.4 | 102.2 | 40.6 | 86.9 | 65.5 | ||

S5 | Positive | 86.6 | 20.4 | 103.9 | 30.6 | 88.5 | 63.7 | 3.64 |

Negative | 61.5 | 12.1 | 104.2 | 30.5 | 96.8 | 62.7 | ||

S6 | Positive | 107.9 | 21.2 | 129.1 | 35.4 | 109.8 | 62.1 | 3.95 |

Negative | 67.9 | 11.4 | 120.6 | 35.6 | 102.5 | 66.8 | ||

S7 | Positive | 91.8 | 25.8 | 109.5 | 46.0 | 93.0 | 62.1 | 2.95 |

Negative | 57.7 | 12.5 | 93.3 | 35.1 | 79.3 | 51.2 |

_{y}and ∆

_{y}are the yielding load and corresponding displacement, respectively; F

_{m}and ∆

_{m}are the peak load and corresponding displacement, respectively; F

_{u}and ∆

_{u}are the ultimate load and corresponding displacement, respectively; μ is the displacement ductility ratio.

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**MDPI and ACS Style**

Chen, S.; Jiang, H.
Experimental Investigation on Seismic Performance of Non-Uniformly Corroded RC Moment-Resisting Frames. *Materials* **2023**, *16*, 2649.
https://doi.org/10.3390/ma16072649

**AMA Style**

Chen S, Jiang H.
Experimental Investigation on Seismic Performance of Non-Uniformly Corroded RC Moment-Resisting Frames. *Materials*. 2023; 16(7):2649.
https://doi.org/10.3390/ma16072649

**Chicago/Turabian Style**

Chen, Shang, and Huanjun Jiang.
2023. "Experimental Investigation on Seismic Performance of Non-Uniformly Corroded RC Moment-Resisting Frames" *Materials* 16, no. 7: 2649.
https://doi.org/10.3390/ma16072649