# Seismic Fragility Curves of RC Buildings Subjected to Aging

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Degradation of Reinforced Concrete Structures

#### 2.1. Damage and Durability

#### 2.2. Corrosion Mechanism

## 3. Seismic Fragility Assessment of Structures

#### 3.1. Fragility Analysis Methods

#### 3.1.1. Multiple-Stripe Analysis

#### 3.1.2. Cloud Analysis

#### 3.1.3. Maximum Likelihood (MLE) Fitting

#### 3.1.4. SPO2IDA Tool

## 4. Past Research on the Fragility Assessment of Corroded RC Structures

## 5. Corrosion Modelling

#### 5.1. Initiation Time of Corrosion

^{2}/s) that depends on the water–cement ratio and the cement type. n is the aging exponent related to the cement type Finally, ${C}_{crit}$ is the critical chloride content, which leads to the depassivation of reinforcing steel (wt%/cement); it depends on the type of steel and the electrochemical environment in concrete. ${C}_{S}$ is the chloride content at the concrete surface.

#### 5.2. Reduction of Rebar Diameter and Ductility

^{2}, where ${v}_{corr}$ (mm/year)$\phantom{\rule{3.33333pt}{0ex}}\approx 0.0116{i}_{corr}$ ($\mathsf{\mu}$A/cm

^{2}), and it is affected by the availability of oxygen and water at the steel surface; therefore, it is related to environmental factors, the concrete quality, and the cover depth. The factor 0.0116 is a conversion factor of $\mathsf{\mu}$A/cm

^{2}into mm/year for steel material [36]. The reduction in the ductility of reinforcement steel is taken into account through the reduction in steel elongation at maximum load. The experimental results provided by Rodriquez and Andrade [37] are used to assess the reduction in the ultimate steel deformation, ${\u03f5}_{su}$. This reduction varies between 30% and 50%, while the loss of the reinforcement’s cross-sectional area varies from 15% to 28%, respectively. Thus, we use linear interpolation when the reinforcement’s cross-sectional reduction is between 15% and 28%, while for values smaller than 15%, we assume that the increase is linear. In other words, if the loss is 22.5%, then the ${\u03f5}_{su}$ reduction is 40%; if the loss is 7.5%, the reduction is 15%.

#### 5.3. Reduction in the Concrete Cover Compressive Strength

## 6. Case Study

#### 6.1. Four-Story RC Building under Corrosion

#### 6.2. Numerical Results

^{2}. The seismic fragility curves of the case study building were obtained using the methodology presented in Section 3. We should note that possible brittle collapse mechanisms (shear failure) of the columns are not considered in the fragility assessment. In all cases, they are estimated, assuming the first-mode spectral acceleration ${S}_{a}({T}_{1},5\%)$ as $IM$ and the maximum roof drift $RDR$ as $EDP$. The fragility curves shown below focus on the moderate damage (LS1) and complete damage (LS3) limit states.

^{2}and ${i}_{corr}$ = 2 $\mathsf{\mu}$A/cm

^{2}, are assumed. Due to the two-dimensional structure, all columns are assumed with the same corrosion rate, even if different values should be adopted for external and internal columns of a three-dimensional structure.

^{2}, cannot affect the fragility curve, even if the cover depth is ${c}_{d}$ = 25 mm. However, ${i}_{corr}$ = 2 $\mathsf{\mu}$A/cm

^{2}always reduces the structural capacity, a point that becomes obvious considering Figure 11b and Figure 12b.

^{2}, and the minimum value for the cover depth, i.e., ${c}_{d}$ = 25 mm.

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Deterioration of RC sections due to (

**a**) chloride-induced and (

**b**) carbonation-induced corrosion of reinforcement.

**Figure 4.**(

**a**) Result of the action of chlorides on an RC beam and (

**b**) reduction in the effective cross-section of the rebars due to corrosion.

**Figure 5.**Deterioration process of reinforcement corrosion [12].

**Figure 6.**The effects of reinforcement corrosion on RC cross-section: (

**a**) uncorroded reinforcement, (

**b**) build-up of corrosion products, (

**c**) cracking, and (

**d**) spalling.

**Figure 10.**Effect of ${i}_{corr}$ on pushover curves, assuming ${c}_{d}$ = 25 mm and (

**a**) t = 50 years, and (

**b**) t = 100 years.

**Figure 11.**Moderate damage (LS1) fragility curves when comparing the different t-values examined when the corrosion rate is equal to (

**a**) ${i}_{corr}$ = 0.1 µA/cm

^{2}and (

**b**) ${i}_{corr}$ = 2 µA/cm

^{2}.

**Figure 12.**Complete damage (LS3) fragility curves when comparing the different t-values examined when the corrosion rate is equal to (

**a**) ${i}_{corr}$ = 0.1 µA/cm

^{2}and (

**b**) ${i}_{corr}$ = 2 µA/cm

^{2}.

**Figure 13.**Fragility curves for constant ${i}_{corr}$ = 2 µA/cm

^{2}and ${c}_{d}$ = 25, 35, 45 mm for (

**a**) LS1 and (

**b**) LS3.

**Table 1.**Influence of aging on the mean of the fragility curves (${\mu}_{lnEDP}$) of different RC structures in terms of percentage modification at 40 to 60 years after construction.

Paper | t | LS1 | LS2 | LS3 | |||
---|---|---|---|---|---|---|---|

Years | Min | Max | Min | Max | Min | Max | |

Karapetrou et al. [16] | 50 | - | - | 0.17 | 0.24 | - | - |

Dizaj et al. [20] | 40 | 0.15 | 0.17 | 0.49 | 0.52 | 0.44 | 0.49 |

Yalciner et al. [22] | 50 | 0.25 | 0.25 | 0.15 | 0.15 | 0.41 | 0.41 |

Couto et al. [24] | 40–60 | 0.11 | 0.17 | - | - | - | - |

Karapetrou et al. [23] | 45 | 0.013 | 0.15 | 0.18 | 0.36 | - | - |

Pugliese and DiSarno [29] | 50 | 0.25 | 0.63 | 0.28 | 0.61 | 0.28 | 0.55 |

**Table 2.**The influence of aging on the fragility curves in terms of percentage modification, considering the evaluation for $CR=10$%.

Paper | CL | LS1 | LS2 | LS3 | |||
---|---|---|---|---|---|---|---|

% | Min | Max | Min | Max | Min | Max | |

Dizaj et al. [18] | 10 | - | - | 0.525 | 0.526 | - | - |

DiSarno & Pugliese [27] | 10 | 0.44 | 0.448 | 0.4 | 0.412 | - | - |

DiSarno & Pugliese [28] | 10 | 0.368 | 0.411 | 0.22 | 0.278 | 0 | 0 |

Parameter | Mean | COV | Distribution |
---|---|---|---|

${k}_{e}$ | 0.676 | 0.17 | Gamma |

${k}_{t}$ | 1.25 | 0.28 | Normal |

${D}_{RCM,0}$ (m^{2}/s) | 1.58 × 10^{−11} | 0.2 | Normal |

${t}_{0}$ (years) | 0.0767 | - | Deterministic |

n | 0.362 | 0.677 | Beta |

${C}_{crit}$ (wt% cement) | 0.6 | 0.25 | Beta |

${C}_{S}$ (wt% cement) | 1.2825 | 0.35 | Normal |

**Table 4.**The influence of aging on the fragility curves in terms of percentage modification, considering the evaluation for 50 and 100 years after the construction of the case study building.

t | ${\mathit{c}}_{\mathit{d}}$ | LS1 | LS2 | LS3 | |||
---|---|---|---|---|---|---|---|

Years | mm | Min | Max | Min | Max | Min | Max |

50 | 25 | 0.00 | 0.21 | 0.00 | 0.22 | 0.00 | 0.22 |

35 | 0.00 | 0.09 | 0.00 | 0.03 | 0.00 | 0.04 | |

45 | 0.00 | 0.04 | 0.00 | 0.05 | 0.00 | 0.06 | |

100 | 25 | 0.00 | 0.40 | 0.00 | 0.49 | 0.00 | 0.51 |

35 | 0.00 | 0.31 | 0.00 | 0.35 | 0.00 | 0.37 | |

45 | 0.00 | 0.18 | 0.00 | 0.19 | 0.00 | 0.19 |

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**MDPI and ACS Style**

Diamantopoulos, S.; Achmet, Z.; Stefanidou, S.; Markogiannaki, O.; Fragiadakis, M.
Seismic Fragility Curves of RC Buildings Subjected to Aging. *GeoHazards* **2024**, *5*, 192-208.
https://doi.org/10.3390/geohazards5010010

**AMA Style**

Diamantopoulos S, Achmet Z, Stefanidou S, Markogiannaki O, Fragiadakis M.
Seismic Fragility Curves of RC Buildings Subjected to Aging. *GeoHazards*. 2024; 5(1):192-208.
https://doi.org/10.3390/geohazards5010010

**Chicago/Turabian Style**

Diamantopoulos, Spyridon, Zeinep Achmet, Sotiria Stefanidou, Olga Markogiannaki, and Michalis Fragiadakis.
2024. "Seismic Fragility Curves of RC Buildings Subjected to Aging" *GeoHazards* 5, no. 1: 192-208.
https://doi.org/10.3390/geohazards5010010