# Enhanced Seismic Retrofit of a Reinforced Concrete Building of Architectural Interest

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Structural Characteristics of the Building

## 3. Seismic Assessment Analysis in Current Condition

_{1}and m

_{2}, with a separation gap at rest width equal to gap

_{r}.

_{H}stiffness, capable of transmitting impact forces, and a non-linear viscous damper with damping coefficient c

_{nl}, reproducing the energy dissipation caused by impact. A second gap element, gap

_{c}, is placed in series with the damper, so as to activate it at the approaching stage of the colliding structures. An elastic spring with stiffness k

_{d}is placed in parallel with the damper, to drive it to its pre-impact position before a new contact occurs.

_{H}of the force-transmitting spring is given by [17]

_{1}(t), u

_{2}(t) are the displacements of the first and second mass, respectively, both functions of time, t, and β is the stiffness parameter providing the spring contact force, F

_{s}, by the following Hertz-type relation [17]:

^{6}kN/m

^{3/2}[18,19]. The damping coefficient of the non-linear damper, c

_{nl}, is defined as [17]

_{nl}. Dampers are denoted by relevant damping coefficients c

_{i}(with i = 1, …, 5) in the multi-linear viscoelastic model scheme drawn in Figure 8.

_{ci}in Figure 8, is placed in series with each damper, which is activated when the connected gap closes and driven to its initial position by a linear spring incorporated in parallel, with stiffness k

_{di}. A non-linear Hertzian spring, with stiffness k

_{HFE}, and the separation gap at rest gap

_{r}, simulating the corresponding components in Jankowski’s scheme, complete the finite element contact model.

_{c}height of 24.55 m above ground. The positions of the four assemblages are visualized in the general and zoomed finite element model views displayed in Figure 9. The overlying pitched roof of Unit 2 is separated by a wider gap from the elevator-stair block of Unit 1; therefore, pounding effects between these building portions are impaired.

_{c}= 24.55 m height of the linked joints of the two units, the tentative value of the maximum interpenetration depth expected from the time-history analysis, δ

_{max,t}—by which the calibration of the finite element contact model is initialized—was fixed at 12.3 mm, i.e., the maximum value of the range (2.5 × 10

^{−4}× H

_{c}= 6.15 mm–5 × 10

^{−4}× H

_{c}= 12.3 mm) located with the above-mentioned criteria [15]. The selection of the upper value is motivated by the dimensions and masses of the two units, which qualify them as medium- to high-rise structures (the minimum value of the range is suggested in [15] for low-rise structures, and the mean value for medium-rise ones). Based on the tentative δ

_{max,t}estimate, all remaining parameters of the contact elements were derived accordingly.

#### 3.1. Modal Analysis

#### 3.2. Time-History and Seismic Performance Assessment Analysis

_{R}), Serviceability Design Earthquake (SDE, with 63%/V

_{R}probability), Basic Design Earthquake (BDE, with 10%/V

_{R}probability) and Maximum Considered Earthquake (MCE, with 5%/V

_{R}probability). The V

_{R}period is fixed at 75 years, which is obtained by multiplying the nominal structural life V

_{N}of 50 years by a coefficient of use C

_{u}equal to 1.5, imposed to buildings with significant crowding conditions, like the case study. The reference site parameters are as follows: topographic category T1 (flat surface), and B-type (medium-hard) soil. Relevant pseudo-acceleration elastic response spectra at linear viscous damping ratio of 5% are plotted in Figure 10.

_{lc,1}–M

_{lc,2}biaxial moment interaction curves—M

_{lc,1}, M

_{lc,2}being the bending moments around the local axes 1 and 2 of columns in plan, with 1 parallel to X, and 2 to Y—graphed by jointly plotting the two bending moment response histories, are presented in Figure 12 for a C21-type column of Unit 2 facing the separation gap at the upper storey (the top section of which is connected to one of the four multi-linear viscoelastic models), and a C20-type column belonging to the first storey of the same unit. As shown in Table 2, the two columns have sides of 400 mm along X and 300 mm along Y (C21), and 400 mm along X and 200 mm along Y (C20). Both columns are reinforced by four Ø16 vertical bars and Ø10 stirrups spaced at 150 mm. The bending moment interaction domains of the two columns, traced out for the value of the axial force referred to the basic combination of gravity loads, are also shown in the two graphs.

_{lc,1}–M

_{lc,2}combined values of around 5.9 (C21) and 3.1 (C20) times greater than the corresponding values situated on the safe domain boundaries. Remarkably unsafe response conditions are checked from the response at the BDE too, with severe pounding conditions determining peak interpenetration depth values of 11.1 mm and nominal unsafety factors in structural members up to 4.3. Around 15% of columns do not pass stress checks even at the SDE, with unsafety factors reaching 1.6.

## 4. Base Isolation Retrofit Hypothesis

_{e}, and the equivalent viscous damping coefficient ratio, ξ

_{e}, of the device are expressed as [5]:

_{DCSS}= effective pendulum length (L

_{DCSS}= 2(R − h) = 2R − 2h, with R = radium of pendulum and h = slider center-to-surface distance), μ = friction coefficient and d

_{max}= maximum displacement of the isolator along all directions in plan.

_{DCSS}= 3100 mm, d

_{max}= ±200 mm, μ = 0.025, T

_{e}= 3.1 s, ξ

_{e}= 15.2%, for all types; N

_{Rd}= maximum allowable vertical force = 1500 kN, D = diameter = 490 mm, H = height = 114 mm—Type-1; N

_{Rd}= 2000 kN, D = 520 mm, H = 109 mm—Type-2; N

_{Rd}= 2500 kN, D = 540 mm, H = 106 mm—Type-3.

#### 4.1. Modal Analysis

_{e}= 3.1 s equivalent period of the isolators given by Equation (5) due to the superstructure deformability contribution to these modes.

#### 4.2. Time-History and Seismic Performance Verification Analysis

_{lc,1}–M

_{lc,2}biaxial moment interaction curves of the C21-type and C20-type columns referred to in Figure 18 highlight that the response is reduced by a factor greater than 10 for the former, which is the most affected by pounding effects in current state, and nearly equal to 10 (C20), thanks to the mitigating action of the base isolation system. This helps in constraining the response curves within the boundary of the M

_{lc,1}–M

_{lc,2}safe interaction domain with wide margins.

^{2}and 400 × 400 mm

^{2}, respectively, are plotted in Figure 19. The greater average width in terms of force of the cycles obtained for the C9-type isolator is a consequence of the notably greater axial force, and thus higher friction forces, acting on it, as compared to the C19-type element. The peak displacements of both isolators, as well as of all remaining ones, are below 140 mm, i.e., considerably smaller than the available device displacements of ±200 mm.

^{2}, i.e., 50% lower than the cost of conventional rehabilitation designs, e.g., based on jacketing with steel profiles or fiber-reinforced plastics of the structural members in unsafe conditions. As the base isolation intervention is confined to the second underground level, it does not cause any intrusion on the superstructure, preserving its architecture and preventing significant interruptions of usage of the building.

## 5. Conclusions

- -
- The Automobile Club Headquarters in Florence, selected as a representative case study for this stock of buildings, showed seismic performance capacities even poorer than expected for ordinary buildings of the same period. This is due to the peculiar characteristics of its structural system, notably irregular both in plan and elevation, with staggered levels in the lower storeys, some of which suspended to cantilevered beams, poor redundancy of several frame members and a 30-mm-wide only technical gap separating the two main constituting wings.
- -
- Indeed, the results of the time-history performance evaluation analysis highlight that around 15% of columns do not pass stress checks even at the serviceability design earthquake level, with unsafety factors reaching 1.6.
- -
- At the same time, severe pounding conditions, as assessed by peak interpenetration depth values of 11.1 mm, as well as generally unsafe conditions of structural members quantified by nominal unsafety factors up to 4.3, are found at the basic design earthquake level.
- -
- The interpenetration depth reaches 14.1 mm at the maximum considered earthquake level, with corresponding total collision forces greater than 13,000 kN, which would cause severe damage to the infills in contact with the columns of the colliding alignments and complete disruption of the concrete cover of relevant beams. In addition, the increase in the stress states of the columns belonging to these alignments and the neighboring zones determines nominal unsafety values equal to around 6.
- -
- The maximum inter-storey drift, assumed as basic damage index for the evaluation of the performance of infills and glazed curtain walls, exceeds 1% of the storey height at all storeys at the MCE. This corresponds to the development of diffused cracks both in the infill panels and the glass panes, requiring extensive post-quake repair works for the former and the complete replacement for the latter.
- -
- The proposed base isolation retrofit intervention guarantees non-pounding response conditions and safe stress states for all members up to the MCE.
- -
- The maximum inter-storey drifts are correspondingly shifted below the operational performance level-related limit of 0.33% of the storey height. This prevents damage to infills, plants, finishes and the other drift-sensitive non-structural elements, including the imposing glazed curtain walls.
- -
- The absence of intrusion in the building interiors guaranteed by the proposed retrofit solution helps in preserving its fine architectural appearance, in addition to the advantages offered to ordinary buildings (i.e., no significant interruption of usage during the execution of works, no architectural obstruction and reduction of floor areas caused by the incorporation of new structural members and/or by the strengthening of the existing ones, etc.).
- -
- In addition, the estimated cost of the intervention is around 50% lower than the cost of conventional rehabilitation designs.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Structural plan of the second through fifth complete floors of the hotel (heights of 14.50 m through 24.55 m above ground).

**Figure 9.**Model view showing the separation gap at rest and zoomed view of the four multi-linear viscoelastic assemblages incorporated between pairs of facing joints of Units 1 and 2.

**Figure 10.**Normative pseudo-acceleration elastic response spectra for Florence and the reference site parameters—horizontal (

**a**) and vertical (

**b**) components.

**Figure 11.**Relative displacement (

**a**) and contact force (

**b**) time-histories of a pair of contacting joints obtained from the most demanding MCE-scaled group of input accelerograms.

**Figure 12.**M

_{lc,1}–M

_{lc,2}biaxial moment interaction curves for a C21-type column on the upper storey (

**a**) and a C20-type column on the first storey; (

**b**) obtained from the most demanding MCE-scaled group of input accelerograms.

**Figure 13.**Plan of the foundations of the building with the positions of the DCSS isolators (highlighted with red circles).

**Figure 14.**Vertical sections of the building denoted as C-C and D-D in Figure 13.

**Figure 16.**Views of the finite element model of the structure incorporating the base isolation system.

**Figure 17.**Relative displacement time-history of the pair of contacting joints referred to in Figure 11 obtained from the most demanding MCE-scaled group of input accelerograms.

**Figure 18.**M

_{lc,1}–M

_{lc,2}interaction curves for the C21-type column (

**a**) and C20-type column (

**b**) referred to in Figure 12 obtained from the most demanding MCE-scaled group of input accelerograms.

**Figure 19.**Response cycles of two isolators placed below a C9-type column (

**a**) and a C19-type column (

**b**) obtained from the most demanding MCE-scaled group of input accelerograms.

Beams | Size (mm × mm) | Half-Span Section | End Sections | Stirrups | ||
---|---|---|---|---|---|---|

Top Bars | Bottom Bars | Top Bars | Bottom Bars | ϕ/Spacing | ||

B1 | 800 × 350 | 2ϕ16 + 4ϕ20 | 2ϕ16 + ϕ20 | 2ϕ16 + 6ϕ20 | 2ϕ16 + 6ϕ20 | ϕ10/150 |

B2 | 600 × 350 | 2ϕ16 | 2ϕ16 | 2ϕ16 | 2ϕ16 | ϕ10/150 |

B3 | 800 × 350 | 4ϕ12 | 4ϕ12 + 3ϕ16 | 4ϕ12 + 5ϕ16 | 4ϕ12 | ϕ10/150 |

B4 | 600 × 350 | 2ϕ12 | 2ϕ12 | 2ϕ12 | 2ϕ12 | ϕ10/150 |

B5 | 800 × 350 | 2ϕ12 | 4ϕ12 | 4ϕ12 | 2ϕ12 | ϕ8/150 |

B6 | 1000 × 350 | 18ϕ22 | 18ϕ22 | 18ϕ22 | 18ϕ22 | ϕ8/150 |

B7 | 600 × 350 | 2ϕ12 | 4ϕ12 | 4ϕ12 | 2ϕ12 | ϕ8/150 |

B8 | 400 × 350 | 2ϕ12 | 4ϕ12 | 4ϕ12 | 2ϕ12 | ϕ8/150 |

B9 | 600 × 300 | 4ϕ12 | 2ϕ12 | 4ϕ12 | 2ϕ12 | ϕ8/150 |

B10 | 350 × 150 | 2ϕ12 | 2ϕ12 | 2ϕ12 | 2ϕ12 | ϕ8/150 |

B11 | 300 × 350 | 2ϕ12 | 4ϕ12 | 4ϕ12 | 2ϕ12 | ϕ8/150 |

B12 | 600 × 350 | 2ϕ16 | 2ϕ16 + 2ϕ12 | 2ϕ16 + 4ϕ12 | 2ϕ16 | ϕ8/150 |

B13 | 300 × 350 | 2ϕ16 | 2ϕ16 + 2ϕ20 | 2ϕ16 + 2ϕ20 | 2ϕ16 | ϕ8/150 |

B14 | 300 × 350 | 2ϕ16 | 3ϕ16 | 3ϕ16 | 2ϕ16 | ϕ10/150 |

B17 | 400 × 350 | 2ϕ16 | 2ϕ16 | 2ϕ16 | 2ϕ16 | ϕ10/150 |

B18 | 500 × 650 | 4ϕ16 | 4ϕ16 | 4ϕ16 | 4ϕ16 | ϕ10/150 |

Columns | Size (mm × mm) | Reinforcing Bars | Stirrups |
---|---|---|---|

C1 | 1100 × 600 | 8ϕ26 | ϕ10/250 |

C2 | 1000 × 600 | 8ϕ26 | ϕ10/250 |

C3 | 1000 × 600 | 8ϕ26 | ϕ10/250 |

C4 | 1000 × 800 | 8ϕ26 | ϕ10/250 |

C5 | 1000 × 800 | 8ϕ26 | ϕ10/250 |

C6 | 1000 × 400 | 6ϕ26 | ϕ10/250 |

C7 | 1000 × 400 | 6ϕ26 | ϕ10/250 |

C8 | 1400 × 800 | 8ϕ30 + 8ϕ20 | ϕ8/200 |

C9 | 1000 × 800 | 8ϕ30 + 10ϕ20 + 4ϕ16 | ϕ8/200 |

C10 | Steel Cable | ϕ22 | − |

C11 | 600 × 300 | 4ϕ20 | ϕ10/200 |

C12 | 400 × 300 | 4ϕ20 | ϕ10/200 |

C13 | 600 × 600 | 8ϕ20 | ϕ10/200 |

C14 | 600 × 600 | 8ϕ20 | ϕ10/200 |

C15 | 600 × 600 | 6ϕ26 | ϕ10/250 |

C16 | 600 × 600 | 4ϕ20 | ϕ10/200 |

C17 | 600 × 400 | 4ϕ20 | ϕ10/200 |

C18 | 1200 × 400 | 8ϕ26 | ϕ10/200 |

C19 | 300 × 300 | 4ϕ20 | ϕ10/150 |

C20 | 400 × 200 | 4ϕ16 | ϕ10/150 |

C21 | 400 × 300 | 4ϕ16 | ϕ10/150 |

Walls | Size (mm × mm) | Reinforcing Bars | Stirrups |
---|---|---|---|

W1 | 1850 × 150 | 14ϕ8 | ϕ12/20 |

W2 | 1850 × 300 | 14ϕ8 | ϕ12/20 |

W3 | 1400 × 300 | 12ϕ8 | ϕ12/20 |

W3 | 1850 × 300 | 14ϕ8 | ϕ12/20 |

W3 | 1850 × 300 | 20ϕ8 | ϕ12/20 |

W3 | 2250 × 300 | 24ϕ8 | ϕ12/20 |

W1 | 1850 × 150 | 14ϕ8 | ϕ12/20 |

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## Share and Cite

**MDPI and ACS Style**

Terenzi, G.; Fuso, E.; Sorace, S.; Costoli, I.
Enhanced Seismic Retrofit of a Reinforced Concrete Building of Architectural Interest. *Buildings* **2020**, *10*, 211.
https://doi.org/10.3390/buildings10110211

**AMA Style**

Terenzi G, Fuso E, Sorace S, Costoli I.
Enhanced Seismic Retrofit of a Reinforced Concrete Building of Architectural Interest. *Buildings*. 2020; 10(11):211.
https://doi.org/10.3390/buildings10110211

**Chicago/Turabian Style**

Terenzi, Gloria, Elena Fuso, Stefano Sorace, and Iacopo Costoli.
2020. "Enhanced Seismic Retrofit of a Reinforced Concrete Building of Architectural Interest" *Buildings* 10, no. 11: 211.
https://doi.org/10.3390/buildings10110211