# Seismic Behavior of a Bridge with New Composite Tall Piers under Near-Fault Ground Motion Conditions

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## Abstract

**:**

## 1. Introduction

## 2. Design Concept of New Composite Tall-Pier Bridge

- Under normal service conditions, the new composite tall pier provides sufficient flexural and torsional stiffness. Meanwhile, the I-shape steel beams are installed along the height of the pier to ensure the overall stability of the structure.
- Under the service level earthquakes (SLEs), the whole bridge is intentionally designed to remain essentially elastic.
- Under the design-based earthquakes (DBEs), the EDMSPs are intentionally designed for energy dissipation while CFST columns are designed to remain elastic. The seismic input energy is dissipated by the hysteretic behavior of the EDMSPs, which in return reduces the stiffness of the pier and mitigates the seismic damage. Only slight damage or inelastic states are allowed for I-shape steel beams.

- The new composite tall piers are supposed to perform as well as the conventional RC box section tall piers subject to the static loads. Meanwhile, due to the vertical axial loads are mainly resisted by the CFST columns, the problem of local bulking in conventional steel pier can be avoided.
- During the earthquakes, the CFST columns are designed to remain elastic with the help of the energy dissipating devices. The EDMSPs yield and dissipate seismic energy and can be replaced quickly. The design concept of seismic resilience for tall-pier bridges can be achieved by proper design.
- The new composite tall piers have the same characteristic of rapid construction as the CFST lattice columns, such as segmental prefabrication, less volume of concrete, easy hoisting and installation. Compared with the construction of traditional RC tall piers, the construction equipment is simpler, and the construction speed can be significantly improved during the turnover and climbing formwork.

## 3. Design of New Composite Tall-Pier Bridge

#### 3.1. Bridge Prototype

#### 3.2. Design Procedure

- The axial load-carrying capacity of the new composite tall pier is equivalent to the prototype pier.
- The height and stiffness in the longitudinal direction of the new composite tall pier are equivalent to the prototype one.

_{y}= 345 MPa) steel tube and C50 (f

_{ck}= 50 MPa) concrete. And the EDMSPs between the CFST columns are made of LYP100 (low-yield point steel, f

_{y}= 100 MPa) steel plate. The mechanical properties of the LYP100 are shown in Table 1. In addition, the Q345 I-shaped steel beams with a sectional dimension of 400 mm × 146 mm × 16.5 mm are installed every 16 m along the height of the pier. Figure 3 shows the configuration of the new composite tall pier.

_{L}and B

_{T}, the thicknesses of steel tube t, can be obtained. Note that due to the numerous interrelated parameters, the values of these parameters are not unique. Therefore, a set of parameters is selected empirically. Then the longitudinal and transverse lengths of EDMSPs, W

_{L}and W

_{T}, the thicknesses of EDMSPs t

_{M}, are obtained based on the equivalent stiffness in the longitudinal direction as shown in Equation (1). Finally, the sectional parameters of the new composite tall pier are determined. The design procedure is presented in Figure 4.

_{C}, E

_{S}, E

_{M}are the elastic modulus of the core concrete, steel tube and EDMSP, respectively. I

_{CL}, I

_{SL}, I

_{ML}are the longitudinal moment of inertia of the core concrete, steel tube and EDMSP, respectively. L is the length of the composite tall pier. K

_{N}is the longitudinal stiffness of the composite tall pier.

## 4. Static Performance Analysis

_{c}is the working load factor of the concrete; N

_{un}is the designed value of the sectional vertical load-bearing capacity; M

_{un}is the design value of the sectional flexural capacity; γ is the importance coefficient, which is taken as 1.1. At the same time, Equation (4) should also be met to ensure the out-of-plane stability:

## 5. Seismic Performance Analysis

#### 5.1. Finite Element Model of the Bridges

_{c}= 30 GPa, f

_{ck}= 50 MPa). The reinforcement is defined by the *rebar keyword (i.e., a method to define a integration point with different material fiber in the beam element section). The Kent-Scott-Park model [38] and the USteel01 model (kinematic hardening elastoplastic uniaxial constitutive model) in the PQ-Fiber subroutine developed by the Department of Civil Engineering of Tsinghua University are adopted for the constitutive models of C40(E

_{c}= 30 GPa, f

_{ck}= 40 MPa) unconfined concrete, and the HRB400 (E

_{s}= 210 GPa, f

_{y}= 400 MPa, and α = 0.01) reinforcement, as shown in Figure 5, respectively. The basin type bearings are simulated by the link elements. The stiffness is infinite along the fixed direction. In the active direction, the bidirectional elastoplastic model is adopted for the link element.

#### 5.2. Modal Analysis

#### 5.3. Ground Motion Input

_{S,30}. Besides, the structures in seismic regions should be designed and constructed based on the following requirements: no-collapse requirement under the DBEs and damage limitation requirement under SLEs. The no-collapse requirement means the bridge should retain its structural integrity and a residual load-carrying capacity after the DBEs. Similarly, the occurrence of damage and the associated limitations of use is not allowed in the damage limitation requirement when the structure subjects to SLEs.

#### 5.4. Seismic Responses under the SLEs

#### 5.5. Seismic Responses under the DBEs

_{m}, Φ

_{u}, Φ

_{y}, M

_{y}indicate the maximum sectional curvature, the ultimate curvature, the yield curvature, yield flexural capacity of the component, respectively; β is the energy dissipation coefficient. For the component subject to compression and bending simultaneously, the accumulated hysteretic energy E

_{h}can be obtained by integrating the bending moment over the curvature within the plastic hinge zones.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Design concept of the new composite tall pier. (

**a**) longitudinal view, (

**b**) transverse view, (

**c**) cross section. CFST: column: concrete-filled steel tubular column.

Yield Strength | Tensile Strength | Elongation Ratio | Impact Property |
---|---|---|---|

100 MPa | 239 MPa | 55% | 193 J |

Critical Section | Load Type | Design Internal Forces | Notes | |
---|---|---|---|---|

Axial Force (kN) | Moment (kN·m) | |||

Left limb (top) | Maximum axial force | 15461 | −3468 | All the results meet the requirements of Equations (2)–(4) |

Minimum axial force | 4368 | −1753 | ||

Maximum moment | 4626 | −1324 | ||

Minimum moment | 15202 | −3897 | ||

Left limb (bottom) | Maximum axial force | 13064 | 924 | |

Minimum axial force | 1967 | 2373 | ||

Maximum moment | 6419 | 3392 | ||

Minimum moment | 8612 | −95 | ||

Right limb (top) | Maximum axial force | 13265 | −2820 | |

Minimum axial force | 3181 | 2731 | ||

Maximum moment | 5521 | 2853 | ||

Minimum moment | 10163 | −3047 | ||

Right limb (bottom) | Maximum axial force | 20660 | −635 | |

Minimum axial force | 8613 | 2788 | ||

Maximum moment | 12887 | 3588 | ||

Minimum moment | 15376 | −1317 |

Mode | Period (s) | Vibration Mode | |
---|---|---|---|

Prototype Bridge | New Bridge | ||

1 | 2.191 | 2.072 | 1st-order transverse symmetrical bending |

2 | 1.676 | 1.635 | 1st-order vertical bending |

3 | 1.262 | 1.243 | 1st-order transverse antisymmetric bending |

Number | Event | Station | d (km) | PGA (g) | PGV/PGA (s) | Site Type |
---|---|---|---|---|---|---|

Eq1 | Chi Chi Taiwan | TCU065 | 0.6 | 0.431 | 1.43 | C |

Eq2 | Imperial Valley 06 | El Centro Array #6 | 1.4 | 0.438 | 0.90 | D |

Eq3 | Imperial Valley 06 | El Centro Array #7 | 0.6 | 0.337 | 1.41 | C |

Eq4 | Loma Prieta | Saratoga-Aloha Ave | 8.5 | 0.512 | 0.80 | C |

Eq5 | Irpinia Italy 01 | Sturno | 10.8 | 0.371 | 1.74 | A |

Eq6 | Chi Chi Taiwan | TCU102 | 1.5 | 0.297 | 3.79 | B |

Eq7 | Duzce Turkey | Duzce | 6.6 | 0.296 | 1.34 | C |

Position | Direction | Average Displacement (cm) | $\frac{{\delta}_{P\mathbf{-}}{\delta}_{N}}{{\delta}_{N}}$ | |
---|---|---|---|---|

Prototype Pier(δ _{P}) | New Pier (δ _{N}) | |||

Top of piers | Longitudinal | 7.49 | 7.39 | 1.1% |

Top of piers | Transverse | 5.46 | 5.12 | 6.7% |

Relative displacement between superstructure and piers | 3.73 | 3.49 | 6.9% |

Pier | Critical Section | Longitudinal | Transverse | ||
---|---|---|---|---|---|

Index | Level | Index | Level | ||

P2 | Bottom | 0.35 | Moderate | 0.29 | Moderate |

Medium | 0.41 | Significant | 0.09 | Slight | |

Top | 0.18 | Slight | 0.00 | No | |

P3 | Bottom | 0.32 | Moderate | 0.39 | Moderate |

Medium | 0.35 | Moderate | 0.06 | Slight | |

Top | 0.16 | Slight | 0.10 | Slight |

Position | Direction | Average Displacement(cm) | $\frac{{\delta}_{P-}{\delta}_{N}}{{\delta}_{N}}$ | |
---|---|---|---|---|

Prototype Pier(δ_{P}) | New Pier (δ_{N}) | |||

Top of piers | Longitudinal | 41.43 | 30.15 | 37.4% |

Top of piers | Transverse | 29.07 | 22.59 | 28.6% |

Relative displacement between superstructure and piers | 22.03 | 18.06 | 21.9% |

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**MDPI and ACS Style**

Cai, Z.; Wang, Z.; Lin, K.; Sun, Y.; Zhuo, W.
Seismic Behavior of a Bridge with New Composite Tall Piers under Near-Fault Ground Motion Conditions. *Appl. Sci.* **2020**, *10*, 7377.
https://doi.org/10.3390/app10207377

**AMA Style**

Cai Z, Wang Z, Lin K, Sun Y, Zhuo W.
Seismic Behavior of a Bridge with New Composite Tall Piers under Near-Fault Ground Motion Conditions. *Applied Sciences*. 2020; 10(20):7377.
https://doi.org/10.3390/app10207377

**Chicago/Turabian Style**

Cai, Zhehan, Zhijian Wang, Kaiqi Lin, Ying Sun, and Weidong Zhuo.
2020. "Seismic Behavior of a Bridge with New Composite Tall Piers under Near-Fault Ground Motion Conditions" *Applied Sciences* 10, no. 20: 7377.
https://doi.org/10.3390/app10207377