# Application of a Non-Invasive Technique for the Preservation of a Fortified Masonry Tower

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## Abstract

**:**

## 1. Introduction

## 2. The Fortified Tower of Cagli

#### 2.1. Historical Survey

#### 2.2. Geometrical Survey

## 3. Ambient Vibration Tests

## 4. Operation Modal Analysis

## 5. Numerical Model and Model Updating

#### 5.1. The Finite Element Model

#### 5.2. Model Updating

## 6. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Geo-localization of Cagli village (Marche region, Central Italy) (

**a**), and external views of the fortified tower (

**b**).

**Figure 2.**Horizontal and longitudinal cross-sections of the fortified tower (dimensions are in meters).

**Figure 4.**Cagli Tower’s modal shapes detected on 19 July 2018 and 21 February 2019 and comparison between FDD and SSI techniques with MAC-matrixes.

**Figure 5.**MAC between the modal vectors extracted by the 2018 and 2019 experimental campaigns with the SSI-PC method.

**Figure 6.**Starting numerical model discretization (

**a**) and the corresponding first three modal shapes (

**b**).

**Figure 7.**Numerical model discretization at the final step (

**a**) and the corresponding first three modal shapes (

**b**).

**Figure 8.**MAC-matrix between the updated FEM and experimental data collected on 19 July 2018 (

**a**) and on 21 February 2019 (

**b**).

**Table 1.**Frequencies, complexities and dampings estimated by FDD and SSI-PC methods (the percentage in brackets indicates the absolute error taking as reference the results of the SSI-PC method).

19 July 2018 | |||||

SSI-PC | FDD | ||||

Mode | Frequencies [Hz] | Complexity [%] | Damping [%] | Frequencies [Hz] | Complexity [%] |

I | 5.24 | 0.20 | 0.94 | 5.22 (0.4%) | 0.70 |

II | 5.61 | 4.59 | 1.37 | 5.62 (0.2%) | 3.18 |

III | 8.31 | 0.63 | 0.51 | 8.30 (0.1%) | 1.04 |

21 February 2019 | |||||

SSI-PC | FDD | ||||

Mode | Frequencies [Hz] | Complexity [%] | Damping [%] | Frequencies [Hz] | Complexity [%] |

I | 5.24 | 0.09 | 1.04 | 5.22 (0.4%) | 0.40 |

II | 5.61 | 1.46 | 1.36 | 5.63 (0.2%) | 4.75 |

III | 8.39 | 0.33 | 0.55 | 8.40 (0.1%) | 2.23 |

Material | Elastic Modulus [MPa] | Poisson’s Ratio [-] | Density [kN/m ^{3}] |
---|---|---|---|

Full bricks and lime mortar | 1500 | 0.4 | 18 |

Cut stones with good bonding | 1740 | 0.4 | 21 |

**Table 3.**Comparison of the modal frequencies and shapes between the starting FEM and the OMA results.

Mode | f_{num} [Hz] | $\mathbf{\Delta}\mathit{f}\mathbf{2018}\mathbf{\left[}\mathit{\%}\mathbf{\right]}$ | MAC 2018 | Numerical Modal Shapes |
---|---|---|---|---|

I | 5.05 | 4.00% | 0.83 | Translational on North direction |

II | 5.56 | 0.89% | 0.68 | Translational on East direction |

III | 7.90 | 4.93% | 0.88 | Torsional |

Mode | f_{num} [Hz] | $\mathbf{\Delta}\mathit{f}\mathbf{2018}\mathbf{[}\mathit{\%}\mathbf{]}$ | MAC 2018 | Numerical Modal Shapes |
---|---|---|---|---|

I | 5.17 | 1.34% | 0.85 | Translational on North direction |

II | 5.70 | 1.60% | 0.68 | Translational on East direction |

III | 8.08 | 2.77% | 0.88 | Torsional |

**Table 5.**Comparison of the modal frequencies and shapes between the final FEM realized and the OMA results obtained by the 2019 field testing.

Mode | f_{num} [Hz] | $\mathbf{\Delta}\mathit{f}\mathbf{2019}$ | MAC 2019 | Numerical Modal Shapes |
---|---|---|---|---|

I | 5.17 | 1.34% | 0.85 | Translational on North direction |

II | 5.70 | 1.60% | 0.71 | Translational on East direction |

III | 8.08 | 3.69% | 0.81 | Torsional |

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**MDPI and ACS Style**

Giordano, E.; Marcheggiani, L.; Formisano, A.; Clementi, F.
Application of a Non-Invasive Technique for the Preservation of a Fortified Masonry Tower. *Infrastructures* **2022**, *7*, 30.
https://doi.org/10.3390/infrastructures7030030

**AMA Style**

Giordano E, Marcheggiani L, Formisano A, Clementi F.
Application of a Non-Invasive Technique for the Preservation of a Fortified Masonry Tower. *Infrastructures*. 2022; 7(3):30.
https://doi.org/10.3390/infrastructures7030030

**Chicago/Turabian Style**

Giordano, Ersilia, Laura Marcheggiani, Antonio Formisano, and Francesco Clementi.
2022. "Application of a Non-Invasive Technique for the Preservation of a Fortified Masonry Tower" *Infrastructures* 7, no. 3: 30.
https://doi.org/10.3390/infrastructures7030030