# Experiences of Dynamic Identification and Monitoring of Bridges in Serviceability Conditions and after Hazardous Events

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## Abstract

**:**

## 1. Introduction

## 2. Operational Modal Analysis and Applications to Bridges

#### 2.1. Basics

#### 2.2. Output-Only Modal Identification of Arch Bridges

- Equation (1) relates the fundamental frequency and the span length s in m without any consideration of the associated mode shape (Figure 2a);
- Equation (2), based on a subset of the available data, applies to the bridges showing vertical antisymmetric mode shapes associated to the fundamental frequency (Figure 2b).

#### 2.3. Model Validation

#### 2.4. Vibration Serviceability Assessment of a Footbridge

- 1 pedestrian walking along the middle of the deck—1p wm—(Figure 8a);
- 1 pedestrian walking along one side of the deck—1p ws;
- 2 pedestrians walking along the middle of the deck—2p wm—(Figure 8b);
- 2 pedestrians walking along one side of the deck—2p ws;
- 5 pedestrians walking along the middle of the deck—5p wm;
- 5 pedestrians walking along one side of the deck—5p ws;
- 10 pedestrians walking along the middle of the deck, one way—10p wo—(Figure 8c);
- 10 pedestrians walking along one side of the deck, return—10p wr;
- 1 pedestrian running along the middle of the deck—1p rm;
- 1 pedestrian running along one side of the deck—1p rs—(Figure 8d);
- 2 pedestrians with a loaded trolley walking along the middle of the deck to simulate the passage of stretcher bearers—2t wm—(Figure 8e);
- 2 pedestrians with a loaded trolley walking along one side of the deck to simulate the passage of stretcher bearers—2t ws;
- 2 pedestrians with a loaded trolley running along the middle of the deck to simulate the passage of stretcher bearers—2t rm;
- 2 pedestrians with a loaded trolley running along one side of the deck to simulate the passage of stretcher bearers—2t rs.

^{2}and 11.47 cm/s

^{2}as maximum values of the horizontal and vertical acceleration, respectively.

## 3. Modal-Based Structural Health Monitoring and Applications to Bridges

#### 3.1. Basics

#### 3.2. Modal-Based Damage Detection

#### 3.3. Traffic-Induced Transient Response

#### 3.4. Compensation of Environmental Effects

## 4. Summary and Final Remarks

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Sample images representative of the tested RC arch bridges (source: maps.google.it).

**Figure 2.**Empirical correlations for the prediction of the fundamental frequency of RC arch bridges (

**a**), the fundamental frequency of RC arch bridges corresponding to an antisymmetric vertical bending mode (

**b**).

**Figure 7.**“Ospedale del Mare” footbridge: singular value plots (continuous colored lines) and identified frequencies (dashed lines).

**Figure 8.**“Ospedale del Mare” footbridge: vibration measurements under pedestrian-induced loadings: 1 walking pedestrian (

**a**), 2 walking pedestrians (

**b**), 10 walking pedestrians (

**c**), 1 running pedestrian (

**d**), 2 walking pedestrians with loaded trolley (

**e**).

**Figure 10.**The bridge model: natural frequency time series in the as-built (

**a**) and retrofitted (

**b**) configuration before and after shaking (adapted from [52]).

**Figure 12.**St. Francesco da Paola revolving bridge in Taranto (

**a**), sample of the acceleration time histories (the early 30 min of the test) clearly showing the passage of heavy vehicles on the bridge—(

**b**), tracking of the fundamental frequencies (

**c**).

**Figure 13.**The Infante D. Henrique bridge (

**a**); comparison between predicted and experimental bridge frequencies depending on time (

**b**); patterns of relevant environmental and operational variables (EOVs) estimated by Second Order Blind Identification (SOBI): temperature (

**c**), humidity (

**d**), and traffic (

**e**).

**Table 1.**Fundamental modal properties of a set of highway RC bridges in Southern Italy (ϕ

_{i}means the i-th mode shape, V is for vertical bending, H is for horizontal bending).

Bridge Number | Total Length (m) | Span Length (m) | Rise Until the Crown (m) | f_{1} (Hz) | ϕ_{1} | f_{2} (Hz) | ϕ_{2} |
---|---|---|---|---|---|---|---|

I | 76.4 | 60.8 | 15.4 | 2.78 | V | 3.62 | H |

II | 76 | 76 | 19.3 | 2.95 | H | 3.04 | V |

III | 60.8 | 60.8 | 18 | 2.85 | V | 3.82 | H |

IV | 140 | 120 | 32.5 | 1.32 | H | 1.45 | V |

V | 60 | 60 | 20.8 | 2.53 | V | 3.38 | H |

**Table 2.**Predictive performance of the empirical correlations for the estimation of the fundamental frequencies of RC arch bridges.

Bridge | Span (m) | f_{exp} (Hz) | f_{corr} (Hz)—Equation (1) | f_{corr} (Hz)—Equation (2) |
---|---|---|---|---|

Montecastelli bridge [30] | 68.7 | 3.18 | 2.89 | 3.01 |

Arch bridge in Portugal [31] | 80 | 2.11 | 2.20 | 2.38 |

Mode | f (Hz) | ξ (%) | Mode Shape Description |
---|---|---|---|

I | 3.75 | 0.7 | Out-of-plane bending |

II | 4.39 | 2.4 | In-plane bending |

III | 5.40 | 1.2 | Torsion |

IV | 5.90 | 2.0 | Out-of-plane bending |

Mode | f_{exp} (Hz) | f_{FEM} (Hz) | Δf (%) | MAC |
---|---|---|---|---|

I | 3.75 | 3.55 | −5 | 0.97 |

II | 4.39 | 3.58 | −18 | 0.97 |

III | 5.40 | 5.97 | 11 | 0.85 |

IV | 5.90 | 6.03 | 2 | 0.87 |

Mode | f (Hz) | ξ (%) | Mode Shape | CrossMAC |
---|---|---|---|---|

I | 1.34 | 0.2 | Horizontal bending | ≈1 |

II | 1.54 | 0.4 | Vertical bending | ≈1 |

III | 2.16 | 0.2 | Vertical bending | ≈1 |

IV | 2.40 | 0.3 | Torsion | ≈1 |

V | 2.62 | 0.3 | Horizontal bending coupled with torsion | ≈1 |

VI | 3.65 | 0.3 | Torsion coupled with transverse displacements | ≈1 |

VII | 4.05 | 0.6 | Vertical bending | ≈1 |

VIII | 4.13 | 0.4 | Vertical bending | 0.98 |

IX | 6.22 | 0.6 | Vertical bending | 0.99 |

X | 7.15 | 1.3 | Vertical bending | 0.99 |

XI | 8.31 | 0.5 | Torsion coupled with transverse displacements | 0.98 |

XII | 9.23 | 0.8 | Vertical bending | 0.99 |

**Table 6.**(a) “Ospedale del Mare” footbridge: maximum recorded acceleration (a

_{max}) in horizontal (a

_{h}) and vertical (a

_{v}) direction under different pedestrian-induced loadings, first passage. (b) “Ospedale del Mare” footbridge: maximum recorded acceleration (a

_{max}) in horizontal (a

_{h}) and vertical (a

_{v}) direction under different pedestrian-induced loadings, second passage.

(a) | ||||||||||||||

a_{max}$\left(\frac{cm}{{s}^{2}}\right)$ | 1p wm | 1p ws | 2p wm | 2p ws | 5p wm | 5p ws | 10p wo | 10p wr | 1p rm | 1p rs | 2t wm | 2t ws | 2t rm | 2t rs |

a_{h} | 0.8 | 1.1 | 1.0 | 1.1 | 1.6 | 2.0 | 2.0 | 1.5 | 1.1 | 2.8 | 1.3 | 2.0 | 1.8 | 2.3 |

a_{v} | 4.3 | 3.6 | 6.1 | 4.8 | 6.2 | 8.8 | 8.8 | 11.4 | 15.8 | 16.1 | 12.1 | 13.5 | 24.8 | 21.2 |

(b) | ||||||||||||||

a_{max}$\left(\frac{cm}{{s}^{2}}\right)$ | 1p wm | 1p ws | 2p wm | 2p ws | 5p wm | 5p ws | 10p wo | 10p wr | 1p rm | 1p rs | 2t wm | 2t ws | 2t rm | 2t rs |

a_{h} | 0.9 | 1.1 | 0.8 | 1.1 | 1.6 | 2.2 | 2.1 | 2.5 | 1.2 | 1.6 | 1.6 | 1.8 | 1.8 | 2.0 |

a_{v} | 3.4 | 3.4 | 4.7 | 4.6 | 5.9 | 7.1 | 7.6 | 8.6 | 16.6 | 17.7 | 12.3 | 13.6 | 21.6 | 22.8 |

**Table 7.**Vertical (a

_{v,limit}) and transverse (a

_{h,limit}) acceleration limits for different comfort levels.

Comfort Level | Description | a_{v,limit} (cm/s^{2}) | a_{h,limit} (cm/s^{2}) | ||
---|---|---|---|---|---|

HIVOSS [37] | SETRA [39] | HIVOSS [37] | SETRA [39] | ||

CL 1 | Maximum | <50 | <50 | <10 | <15 |

CL 2 | Medium | 50 ÷ 100 | 50 ÷ 100 | 10 ÷ 30 | 15 ÷ 30 |

CL 3 | Minimum | 100 ÷ 250 | 100 ÷ 250 | 30 ÷ 80 | 30 ÷ 80 |

CL 4 | Unacceptable | >250 | >250 | >80 | >80 |

**Table 8.**St. Francesco da Paola revolving bridge: average value (f

_{av}) and standard deviation (σ

_{f}) of the automatically identified natural frequencies in comparison with the result of traditional Operational Modal Analysis (OMA) applied to a sample dataset.

Mode | Traditional OMA (Single Dataset) f (Hz) | Automated OMA (Multiple Datasets) f _{av} (σ_{f}) (Hz) |
---|---|---|

1 | 2.22 | 2.22 (0.02) |

2 | 2.70 | 2.77 (0.03) |

3 | 4.15 | 4.19 (0.02) |

4 | 7.77 | 7.70 (0.07) |

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**MDPI and ACS Style**

Rainieri, C.; Notarangelo, M.A.; Fabbrocino, G.
Experiences of Dynamic Identification and Monitoring of Bridges in Serviceability Conditions and after Hazardous Events. *Infrastructures* **2020**, *5*, 86.
https://doi.org/10.3390/infrastructures5100086

**AMA Style**

Rainieri C, Notarangelo MA, Fabbrocino G.
Experiences of Dynamic Identification and Monitoring of Bridges in Serviceability Conditions and after Hazardous Events. *Infrastructures*. 2020; 5(10):86.
https://doi.org/10.3390/infrastructures5100086

**Chicago/Turabian Style**

Rainieri, Carlo, Matilde A. Notarangelo, and Giovanni Fabbrocino.
2020. "Experiences of Dynamic Identification and Monitoring of Bridges in Serviceability Conditions and after Hazardous Events" *Infrastructures* 5, no. 10: 86.
https://doi.org/10.3390/infrastructures5100086