# Enhancing Seismic Resilience of Existing Reinforced Concrete Building Using Non-Linear Viscous Dampers: A Comparative Study

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## Abstract

**:**

## 1. Introduction

_{v}is the velocity-based ground response coefficient for specific seismic zones and soil profiles. R is the response modification factor for lateral force-resisting systems. T is the fundamental time. W is the weight of the building.

_{s}(mapped spectral acceleration of short period at 2% probability of exceedance in 50 years) and S

_{1}(mapped spectral acceleration of long period at 2% probability of exceedance in 50 years) are given to each site. According to the BCP 2021, the formula used to calculate the base shear (V) is shown in Equation (2).

_{s}, F

_{a}, I, R, and W are the design spectral acceleration parameter, site coefficient, occupancy importance, response modification factor, and weight of the building, respectively.

#### Research Significance

## 2. Case Study Building

## 3. Seismic Fortification of Existing Buildings

#### 3.1. Lateral Bracing System

#### 3.2. Seismic Retrofit Jacketing

#### 3.3. Dampers

#### 3.3.1. Fluid Viscous Damper

#### Components of Fluid Viscous Dampers

#### Characteristics of Fluid Viscous Dampers

_{d}is the velocity between two ends of the damper, α is an exponent that depends on the fluid’s viscosity properties and the piston’s viscosity, and t is time—the seismic energy during an earthquake. The exponent ‘α ’ in the equation determines the P value in fluid viscous dampers (FVDs), which can be equal to or less than one. An exponent of α = 1 characterizes a linear viscous damper, whereas a non-linear FVD has an exponent of α < 1, which effectively reduces high-velocity shocks. Conversely, dampers with an exponent of α > 1 are not commonly observed in practical applications. It is important to carefully evaluate the appropriate type of FVD for a specific structure based on its behavior and desired performance [73]. Figure 5a,b show the force–velocity and displacement plots for a linear and non-linear viscous damper. As observed in Figure 5b, a non-linear viscous dashpot can dissipate more energy than a linear viscous damper when oscillated to the same level of displacement and with the same peak force (represented by the area enclosed within the force–displacement curve).

#### Design of Non-Linear Fluid Viscous Dampers

_{0}represents the natural damping ratio of a system in the absence of dampers, ξ

_{d}represents the damping ratio introduced by the mufflers. In the case of reinforced concrete structures, the inherent damping ratio is typically assumed to be 5%, whereas the dense damping ratio for non-linear viscous dampers is selected based on the desired level of damping. Once a value of the damping ratio ξ

_{d}is determined, an estimate for the damping coefficient C of non-linear devices in a diagonal arrangement can be calculated by the following Equation (5), given by FEMA 274.

_{d}is the damping ratio of a system that is equivalent to the damping contributed by non-linear dampers, A is the parameter of velocity, C

_{j}= damping coefficient of damper j, m

_{i}= mass of floor I, θ

_{j}= inclination angle of damper j, Φ

_{i}= mode displacement at the floor I, Φ

_{rj}= relative horizontal displacement of damper j, A = amplitude, w = angular frequency, and α = damping coefficient.

## 4. Non-Linear Modeling of Case Study’s Building

#### Dampers Location

## 5. Selection of Ground Motions

## 6. Results and Discussions

#### 6.1. Displacement and Drift Responses

#### 6.2. Acceleration Responses

#### 6.3. Time Histories Responses

#### 6.4. Energy Dissipation

## 7. Conclusions

- Compared to other types of retrofitting techniques, such as lateral bracing systems and seismic retrofitting jacketing, FVDs have the advantage of being relatively easy to install, requiring minimal maintenance, and having a long service life. Additionally, FVDs can be integrated into the existing structural system of a building without significantly altering its appearance or function, which may not be the case with other retrofitting techniques.
- The seismic retrofitting of the case study building with non-linear FVDs has improved its performance in terms of displacement, inter-story drift, and acceleration response against seismic loadings significantly.
- Installing FVDs in the end bays of the structures/buildings is more beneficial because it reduces the displacement by 36.58% and the inter-story drift by 31.16%. It also resists the torsion of the building.
- The addition of the non-linear viscous damper to the building had no significant effect on the floor acceleration of the building compared to the building without the non-linear fluid viscous dampers.
- The fundamental time period of the building with non-linear viscous dampers decreased by 0.51 (s) more than the building without a non-linear viscous damper. This is because of the increased stiffness of the building.
- More than 70% of the energy is dissipated by FVDs in the controlled retrofitted structure against all three seismic loading cases. In addition, in the retrofitted structure of FVDs, the structural elements, i.e., columns, beams, and shear walls, remain safe against inelastic yielding.
- Overall, this study suggests that retrofitting existing buildings with non-linear FVDs is a promising approach that significantly improves the seismic reliance of the structure in seismic-prone areas.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Comparison of the responses of the structure according to BCP 2007 and BCP 2021. (

**a**) Displacement response, (

**b**) inter-story drift response, (

**c**) shear force response, and (

**d**) moment response.

**Figure 4.**A labelled figure showcases the inner workings of a typical fluid viscous damper (FVD). Reprinted with permission from [67].

**Figure 5.**(

**a**) Force velocity relationship of FVDs. (

**b**) Force displacement relationship of FVDs. In the case of linear dampers, the damper force increases linearly with the damper velocity, as shown in (

**a**). In the case of a non-linear damper, the damper force decreases with an increase in the damper velocity. Similarly, non-linear viscous dampers dissipate more energy than linear viscous dampers at the same excitation. Reprinted with permission from [74].

**Figure 6.**(

**a**) A 3D finite element model of the building in Perform 3D without fluid viscous damper, and (

**b**) bay of structure without dampers. (

**c**) A 3D finite element model of building with fluid viscous damper, and (

**d**) bay of structure with fluid viscous damper.

**Figure 8.**(

**a**,

**b**) Time histories of Coalinga−01 (1983) recording station Parkfield−Cholame 2E in H1 and H2 direction, respectively. (

**c**,

**d**) Time histories of Coalinga−01 (1983) recording station Parkfield −Stone Corral 2E in H1 and H2 direction, respectively. (

**e**,

**f**) Time histories of Northridge−01 (1994) recording station Palmdale–Hwy 14 and Palmdale in H1 and H2 direction, respectively.

**Figure 9.**Modal deformed shape of the building with and without non-linear fluid viscous dampers for (

**a**,

**d**) mode 1, (

**b**,

**e**) mode 2, and (

**c**,

**f**) mode 3.

**Figure 10.**Displacement responses of the structure with and without fluid viscous dampers under seismic loadings: (

**a**) Coalinga-01 (Parkfield–Cholame 2E), (

**b**) Coalinga-01 (Parkfield–Stone Corral 2E), and (

**c**) Northridge-01 (Palmdale–Hwy 14 and Palmdale).

**Figure 11.**Drift responses of the structure with and without fluid viscous dampers under seismic loadings (

**a**) Coalinga-01 (Parkfield–Cholame 2E), (

**b**) Coalinga-01 (Parkfield–Stone Corral 2E), and (

**c**) Northridge-01 (Palmdale–Hwy 14 and Palmdale).

**Figure 12.**Acceleration responses of the structure with and without fluid viscous dampers under seismic loadings (

**a**) Coalinga-01 (Parkfield–Cholame 2E), (

**b**) Coalinga-01 (Parkfield–Stone Corral 2E), and (

**c**) Northridge-01 (Palmdale–Hwy 14 and Palmdale).

**Figure 13.**Acceleration time−history responses of the top story with and without fluid viscous dampers under (

**a**) Coalinga−01 (Parkfield−Cholame 2E), (

**b**) Coalinga−01 (Parkfield−Stone Corral 2E), and (

**c**) Northridge−01 (Palmdale−Hwy 14 and Palmdale).

**Figure 14.**Displacement time−history responses of the top story with and without fluid viscous dampers under (

**a**) Coalinga−01 (Parkfield−Cholame 2E), (

**b**) Coalinga−01 (Parkfield−Stone Corral 2E), and (

**c**) Northridge−01 (Palmdale−Hwy14 and Palmdale).

**Figure 15.**Percentage (% age) energy dissipation of structural elements of the buildings with and without fluid viscous dampers under (

**a**) Coalinga−01 (Parkfield–Cholame 2E), (

**b**) Coalinga−01 (Parkfield−Stone-Corral 2E), and (

**c**) Northridge−01 (Palmdale−Hwy14 and Palmdale).

BCP 2007 Parameters | BCP 2021 Parameters | ||
---|---|---|---|

Seismic Zone | 2B | Short-period spectral acceleration (S_{s}) | 1.302 |

Closest distance to the seismic source (km) for N_{a} | > 10 | Long-period spectral acceleration (S_{1}) | 0.381 |

Closest distance to the seismic source (km) for N_{v} | > 15 | Site coefficient (F_{a}) | 1 |

Near source factor (N_{a}) | 1 | Site coefficient (F_{v}) | 1.91904 |

Near source factor (N_{v}) | 1 | Site-modified spectral acceleration (SMS) | 1.302 |

Seismic zone factor (Z) | 0.2 | Site-modified spectral acceleration (SM1) | 0.731 |

Seismic coefficient (C_{a}) | 0.28 | Design-level spectral acceleration (SDS) | 0.868 |

Seismic coefficient (C_{v}) | 0.4 | Design-level spectral acceleration (SD1) | 0.487 |

Building Height (m) | 33 | |

No. of Stories | 9 | |

Specified compressive strength of concrete f’c (MPa) | RC columns | 35 |

RC beams and slabs | 20.68 | |

RC walls | 27.57 | |

Specified yield strength of longitudinal steel bar in RC walls and RC columns fy (MPa) | 414 | |

Natural period of vibrational modes (s) | Mode 1 (X direction) | 1.34 |

Mode 2 (Y direction) | 1.18 | |

Mode 3 (Torsional) | 0.87 |

Earthquake Name (year) | Station Name | Magnitude | Mechanism | Rjb (km) | Rrup (km) | Vs30 (m/s) |
---|---|---|---|---|---|---|

Coalinga-01 (1983) | Parkfield–Cholame 2E | 6.36 | Reverse | 41.99 | 42.92 | 522.74 |

Coalinga-01 (1983) | Parkfield–Stone Corral 2E | 6.36 | Reverse | 35.29 | 36.4 | 566.33 |

Northridge-01 (1994) | Palmdale–Hwy 14 and Palmdale | 6.69 | Reverse | 41.37 | 41.67 | 551.56 |

Structure without Dampers | Structure with Dampers | |
---|---|---|

Modal Participation Mass Ratio | Modal Participation Mass Ratio | |

Mode 1 (Ux) | 0.5921 | 0.6086 |

Mode 2 (Uy) | 0.5790 | 0.6079 |

Mode 3 (Rz) | 0.5244 | 0.5471 |

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## Share and Cite

**MDPI and ACS Style**

Riaz, R.D.; Malik, U.J.; Shah, M.U.; Usman, M.; Najam, F.A.
Enhancing Seismic Resilience of Existing Reinforced Concrete Building Using Non-Linear Viscous Dampers: A Comparative Study. *Actuators* **2023**, *12*, 175.
https://doi.org/10.3390/act12040175

**AMA Style**

Riaz RD, Malik UJ, Shah MU, Usman M, Najam FA.
Enhancing Seismic Resilience of Existing Reinforced Concrete Building Using Non-Linear Viscous Dampers: A Comparative Study. *Actuators*. 2023; 12(4):175.
https://doi.org/10.3390/act12040175

**Chicago/Turabian Style**

Riaz, Raja Dilawar, Umair Jalil Malik, Mati Ullah Shah, Muhammad Usman, and Fawad Ahmed Najam.
2023. "Enhancing Seismic Resilience of Existing Reinforced Concrete Building Using Non-Linear Viscous Dampers: A Comparative Study" *Actuators* 12, no. 4: 175.
https://doi.org/10.3390/act12040175