# Inspection and Structural Rehabilitation of an Existing Masonry Arch Railway Bridge

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Bridge Location and Historical Background

#### 2.2. Geometrical Data and Materials

#### 2.3. Mechanical Properties of Materials

#### 2.4. Modeling Assumptions

_{t}) and compressive strength (f

_{c}) of squared stone block masonry and solid brick and lime mortar masonry; compressive fracture energy (G

_{c}); tensile fracture energy (G

_{f}); mesh size (h).

## 3. Seismic Vulnerability Analysis and Results

#### 3.1. Modal Analysis

#### 3.2. Pushover Analysis

#### 3.3. Result of Pushover Analysis

_{max}is the displacement capacity of the structure and d

_{max}is the required displacement of the actual MDOF system. This displacement is obtained by multiplying the required displacement of the equivalent system ${\mathrm{d}}_{\mathrm{max}}^{*}$ by the modal participation factor Γ (d

_{max}= Γ${\mathrm{d}}_{\mathrm{max}}^{*}$). The required displacement of the equivalent system is a function of the initial proper period associated with the elastic range T* and it is evaluated using Equation (2) if T* ≥ T

_{c}or Equation (3) if T* ≤ T

_{c}:

_{max}for the four MDOF capacity curves are the following:

- MDOF Capacity Curve Push. long. mode: U
_{max}= 7.6 mm; - MDOF Capacity Curve Push. long. masses: U
_{max}= 10.4 mm; - MDOF Capacity Curve Push. trans. mode: U
_{max}= 7.1 mm; - MDOF Capacity Curve Push. trans. masses: U
_{max}= 7.2 mm.

- equivalent bilinear Push. long. mode: q* = 2.2 < 3;
- equivalent bilinear Push. long. masses: q* = 1.53 < 3;
- equivalent bilinear Push. trans. mode: q* = 3.88 > 3;
- equivalent bilinear Push. trans. masses: q* = 1.25 < 3.

#### 3.4. Seismic Vulnerability in Terms of Acceleration

_{E,min}is the minimum seismic risk index among those associated with local and global collapse mechanisms.

#### 3.4.1. Global Risk Indexes

_{g,C}(seismic capacity), to the peak ground acceleration at the site where the structure rises, a

_{g,D}(seismic demand). To assess the seismic capacity, an iterative procedure was performed to identify, for the four pushover analyses, the seismic spectrum for which the demand d

_{max}equals the displacement capacity U

_{max}(capacity spectrum) and the corresponding value of the behavior factor q*.

#### 3.4.2. Local Risk Indexes

_{m}equal to the ratio between the area of the spandrel A

_{t}= 46.6 m

^{2}and its length L. After performing the calculations, a risk index associated with the overturning mechanism of the spandrel wall 𝜁

_{E, loc}= 3.9 was obtained.

#### 3.4.3. Seismic Vulnerability Verification

_{E,min}= 0.51 < 1. Since 𝜁

_{E,min}< 1, the seismic vulnerability verification of the bridge ante operam is “not satisfied”.

## 4. Design of Structural Rehabilitation

#### 4.1. New Modeling Assumption

_{yk}= 450 N/mm

^{2}: characteristic yield strength; γ

_{s}= 1.15: partial factor for reinforcing steel; f

_{yd}= 391.3 N/mm

^{2}: design yield strength; k: ratio of tensile strength to the yield stress of the steel; E

_{s}= 200 GPa: design value of the elasticity modulus; f

_{td}: design value of tensile strength; ε

_{uk}: characteristic strain of steel reinforcement at maximum force; ε

_{ud}: design strain of steel reinforcement at maximum force, according to Eurocode 2 [17] and shown in Figure 15).

#### 4.2. Constitutive Models

#### 4.3. Post Operam Modal Analysis

#### 4.4. Post Operam Pushover Analysis

#### 4.5. Check Post Operam Pushover Analysis

_{B}. Therefore, for all cases, Equation (3) should be used for seismic verification. Table 3 shows the verification results. As required by current codes, having obtained U

_{max}> d

_{max}for each pushover analysis performed, the verification in terms of displacement is “satisfied”.

#### 4.6. Post Operam Seismic Vulnerability

_{E,min}= 1.38 at the push analysis. transv. mode. Since no spandrel wall reinforcement interventions were performed, as they were not necessary, the post operam local risk index is the same as the ante operam one.

#### Result of the Post Operam Assessment

_{E,min}= 1.38 > 1. With 𝜁

_{E,min}> 1, the seismic vulnerability check of the upgraded bridge is “satisfied”.

#### 4.7. Checking of the Injected Anchors

_{bm}) shown in Figure 21.

## 5. 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.**(

**a**) Acerenza–Avigliano Lucania line inaugurated on 26 May 1930 [9]. (

**b**) Concrete coating at the bottom of the vault.

**Figure 5.**(

**a**) Geometric model of the bridge. (

**b**) Parabolic (

**left**) and linear (

**right**) constitutive model [12].

**Figure 6.**(

**a**) Main mode shape in longitudinal direction (T = 0.25 s). (

**b**) Main mode shape in transverse direction (T = 0.24 s).

**Figure 7.**(

**a**) Push. long. mode: Pre operam MDOF capacity curve. (

**b**) Push. long. masses: Pre operam MDOF capacity curve.

**Figure 8.**(

**a**) Push. transv. mode: Pre operam MDOF capacity curve. (

**b**) Push. transv. masses: Pre operam MDOF capacity curve.

**Figure 9.**(

**a**) Push. long. mode: Pre operam equivalent bilinear. (

**b**) Push. long. masses: Pre operam equivalent bilinear.

**Figure 10.**(

**a**) Push. transv. mode: Pre operam equivalent bilinear. (

**b**) Push. transv. masses: Pre operam equivalent bilinear.

**Figure 14.**(

**a**) Geometric model of the post operam bridge. (

**b**) Geometric model of the reinforcements and anchors.

**Figure 16.**(

**a**) Post operam main mode shape in longitudinal direction (T = 0.158 s); (

**b**) post operam main mode shape in transverse direction (T = 0.147 s).

**Figure 17.**(

**a**) Push. long. mode: pre and post operam MDOF capacity curve. (

**b**) Push. long. masses: pre and post operam MDOF capacity curve.

**Figure 18.**(

**a**) Push. trans. mode: pre and post operam MDOF capacity curve. (

**b**) Push. trans. masses: pre and post operam MDOF capacity curve.

**Figure 19.**(

**a**) Push. long. mode: post operam equivalent bilinear. (

**b**) Push. long. masses: post operam equivalent bilinear.

**Figure 20.**(

**a**) Push. trans. mode: post operam equivalent bilinear. (

**b**) Push. trans. masses: post operam equivalent bilinear.

Element | Masonry Typology | f_{d} (N/mm ^{2}) | τ_{0d} (N/mm ^{2}) | f_{v0d} (N/mm ^{2}) | E_{d} (N/mm ^{2}) | G_{d} (N/mm ^{2}) | w (kN/m ^{3}) |
---|---|---|---|---|---|---|---|

Abutment, piles, spandrels, foundations | square stone block masonry | 5.83 | 0.09 | 0.19 | 2375 | 793 | 22 |

Arches | solid brick masonry and lime mortar | 2.88 | 0.08 | 0.17 | 1250 | 417 | 18 |

Backfill | disordered rubble stone masonry | 1.25 | 0.02 | - | 725 | 263 | 19 |

_{d}= average compressive strength; τ

_{0d}and f

_{v0d}= average shear strength under zero compressive stress (diagonal tensile failure for irregular and regular texture, respectively); E

_{d}= average value of normal modulus of elasticity; G

_{d}= average value of tangential modulus of elasticity; w = average specific gravity.

Pushover Analysis | T_{R} ^{(a)}(Years) | q* | F_{0} ^{(b)} | T_{C}* (s) | a_{g,C} (g) | a_{g,D} (g) | ζ_{E} |
---|---|---|---|---|---|---|---|

Push. long. mode | 299 | 1.81 | 2.415 | 0.355 | 0.167 | 0.202 | 0.83 |

Push. long. masses | 816 | 1.78 | 2.439 | 0.394 | 0.246 | 0.202 | 1.22 |

Push. trans. mode | 104 | 1.94 | 2.389 | 0.333 | 0.103 | 0.202 | 0.51 |

Push. trans. masses | 465 | 1.24 | 2.445 | 0.363 | 0.200 | 0.202 | 0.99 |

^{(a)}T

_{R}= return period;

^{(b)}F

_{0}= maximum value of the amplification factor of the spectrum in horizontal acceleration.

Pushover Analysis | q* | ${\mathbf{q}}_{\mathbf{ass}}^{*}$^{(a)} | Displacement Demand | ${\mathbf{d}}_{\mathbf{max}}^{*}$ (mm) | d_{max}(mm) | U_{max} (mm) |
---|---|---|---|---|---|---|

Push. long. mode | 1.13 | 1.13 | ${d}_{max}^{*}=\frac{{S}_{De}\left({T}^{*}\right)}{{q}_{ass}^{*}}\left[1+\left({q}_{ass}^{*}-1\right)\frac{{T}_{C}}{{T}^{*}}\right]\ge {S}_{De}\left({T}^{*}\right)$ | 4.48 | 5.65 | 10.4 |

Push. long. masses | 0.80 | 1.00 | 4.52 | 5.70 | 13.5 | |

Push. trans. mode | 1.26 | 1.26 | 5.92 | 6.81 | 11.0 | |

Push. trans. masses | 0.68 | 1.00 | 2.28 | 2.62 | 12.3 |

^{(a)}${\mathrm{q}}_{\mathrm{ass}}^{*}$ ≥ 1.00: assigned structure factor of the equivalent system.

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**MDPI and ACS Style**

Bencardino, F.; Curto, R.; Scavelli, V.
Inspection and Structural Rehabilitation of an Existing Masonry Arch Railway Bridge. *Appl. Sci.* **2023**, *13*, 2973.
https://doi.org/10.3390/app13052973

**AMA Style**

Bencardino F, Curto R, Scavelli V.
Inspection and Structural Rehabilitation of an Existing Masonry Arch Railway Bridge. *Applied Sciences*. 2023; 13(5):2973.
https://doi.org/10.3390/app13052973

**Chicago/Turabian Style**

Bencardino, Francesco, Roberta Curto, and Vincenzo Scavelli.
2023. "Inspection and Structural Rehabilitation of an Existing Masonry Arch Railway Bridge" *Applied Sciences* 13, no. 5: 2973.
https://doi.org/10.3390/app13052973