# Dynamic Response Evaluation of Bridges Considering Aspect Ratio of Pier in Near-Fault and Far-Fault Ground Motions

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Near-Fault and Far-Fault Ground Motions

#### 2.1. Collection of Ground Motions

#### 2.2. Ground Motions with Soil Conditions

_{s30}). KDS and RPA 99/2003 use the shear wave velocity (V

_{s}) in the range of bedrock depths (H) from 10 to 20 m to define the site classifications.

## 3. Configuration and Numerical Modeling of the Bridge

#### 3.1. Bridge Configuration and Design

#### 3.2. Numerical Modeling for the Bridge

## 4. Nonlinear Static Analysis

## 5. Modal Analysis of Bridge

## 6. Seismic Response Characteristics by Nonlinear Dynamic Analyses

#### 6.1. Displacement and Moment of the Bridge

#### 6.2. Analysis of Maximum Displacement

#### 6.3. Analysis of Maximum Moment

#### 6.4. Analysis of the Variations of the Natural Frequency

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Typical time histories of the near-fault ground motion with forward-directivity and fling-step effects and the far-fault ground motion: (

**a**) Near-fault ground motion with forward directivity; (

**b**) near-fault ground motion with fling step; (

**c**) far-fault ground motion

**Figure 2.**Spectral accelerations obtained from site response analyses for seven ground motions defined at the near and far faults: (

**a**) Spectral accelerations for near-fault ground motions; (

**b**) spectral accelerations for far-fault ground motions

**Figure 6.**Stress–strain curves for the inelastic material model: (

**a**) Mander et al. (1988) model; (

**b**) Menegotto and Pinto (1973) model.

**Figure 11.**Relationship of the displacement spectrum (S

_{d}) and maximum lateral displacement with the pier height for near-fault ground motions: (

**a**) Displacement spectrum at near-fault ground motion; (

**b**) maximum displacement at near-fault ground motion.

**Figure 12.**Relationship of the displacement spectrum (S

_{d}) and maximum lateral displacement with the pier height for far-fault ground motions: (

**a**) Displacement spectrum at far-fault ground motion; (

**b**) maximum displacement at far-fault ground motion

**Figure 13.**Maximum moment with increasing bridge height: (

**a**) Maximum moment under near-fault ground motion; (

**b**) Maximum moment under far-fault ground motion.

**Figure 15.**Relationship between the decrease in the natural frequency and the dynamic response ratio (DR): (

**a**,

**b**) The decrease in the natural frequency and the dynamic response ratio at each ground motions.

Name | Country | Year | Magnitude (M) | Distance (km) | PGA (g) | Mean Period (s) | V_{s30} (m/s) | Type of Effect |
---|---|---|---|---|---|---|---|---|

Gyeongju | Korea | 2016 | 5.8 | 9.1 | 0.41 | 0.15 | 610 | FD |

Pohang | Korea | 2017 | 5.4 | 9.5 | 0.27 | 0.48 | 750 | FD |

Northridge | America | 1994 | 6.69 | 5.92 | 0.43 | 0.15 | 628.99 | FD |

Sierra Madre | America | 1991 | 5.61 | 10.36 | 0.28 | 0.25 | 680.37 | FD |

Chi-Chi | Taiwan | 2016 | 7.62 | 11.48 | 0.44 | 0.18 | 665.2 | FS |

Loma Prieta | America | 1989 | 6.93 | 12.69 | 0.26 | 0.49 | 671.77 | FS |

Kocaeli | Turkey | 1999 | 7.4 | 3.2 | 0.63 | 0.26 | 691.34 | FS |

Name | Country | Year | Magnitude (M) | Distance (km) | PGA (g) | Mean Period (s) | V_{s30} (m/s) |
---|---|---|---|---|---|---|---|

EHMH01010324 | Japan | 2001 | 6.4 | 119 | 0.098 | 0.12 | 743 |

Big Bear-01 | America | 1992 | 6.46 | 95.94 | 0.035 | 0.44 | 624.01 |

Chi-Chi | Taiwan | 1999 | 7.62 | 109.27 | 0.080 | 0.97 | 856.38 |

Hector Mine | America | 1999 | 7.13 | 96.91 | 0.033 | 0.62 | 642.83 |

Denali | America | 2002 | 7.9 | 239.52 | 0.0094 | 0.96 | 708.02 |

Tottori | Japan | 2000 | 6.61 | 101.82 | 0.078 | 0.15 | 677.44 |

Niigata | Japan | 2004 | 6.63 | 100.45 | 0.031 | 0.11 | 849.01 |

**Table 3.**Soil types specified in EC 8 (Eurocode 8), UBC 97 (Uniform Building Code), KDS (Korean Design Standard), and RPA 99/2003 (Regles Parasismiques Algeriennes).

Eurocode 8 | UBC 97 | KDS | RPA 99/2003 |
---|---|---|---|

Soil type A: V_{s30} ≥ 800 m/s | Soil type A: V_{s30} ≥ 1500 m/s | S1: H < 1 m | S1: V_{s} > 800 m/s |

Soil type B: 360 ≤ V_{s30} < 800 m/s | Soil type B: 760 ≤ V_{s30} < 1500 m/s | S2: 1 ≤ H ≤ 20 m V_{s} ≥ 260 m/s | S2: 400 ≤ V_{s} < 800 m/s |

Soil type C: 180 ≤ V_{s30} < 360 m/s | Soil type C: 360 ≤ V_{s30} < 760 m/s | S3: 1 ≤ H≤20 m V_{s} < 260 m/s | S3: 200 ≤ V_{s} < 400 m/s |

Soil type D: V_{s30} ≤ 180 m/s | Soil type D: 180 ≤ V_{s30} < 360 m/s | S4: H > 20 m V_{s} ≥ 180 m/s | S4: 100 ≤ V_{s} < 200 m/s |

Soil type E: A soil profile consisting of a surface alluvium layer with V_{s30} values of class C or D and thickness varying between about 5 and 20 m, underlain by stiffer material with V_{s30} > 800 m/s | Soil type E: V_{s30} < 180 m/s | S5: H > 20 m V_{s} < 180 m/s | |

Soil type F: Soils requiring site-specific evaluation | S6: Soils requiring site-specific evaluation |

**Table 4.**Summary of the yield and ultimate displacements and the shear force for the piers of a bridge.

Pier Height (m) | Yield Displ. (${\mathit{D}}_{\mathit{y}}$, mm) | Ultimate Displ. (${\mathit{D}}_{\mathit{y}}$, mm) | Max Shear Force ($\mathit{F}$, kN) |
---|---|---|---|

5 | 22 | 91 | 7200 |

10 | 88 | 215 | 3600 |

15 | 193 | 367 | 2400 |

20 | 361 | 548 | 1800 |

25 | 563 | 720 | 1420 |

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**MDPI and ACS Style**

An, H.; Lee, J.-H.; Shin, S.
Dynamic Response Evaluation of Bridges Considering Aspect Ratio of Pier in Near-Fault and Far-Fault Ground Motions. *Appl. Sci.* **2020**, *10*, 6098.
https://doi.org/10.3390/app10176098

**AMA Style**

An H, Lee J-H, Shin S.
Dynamic Response Evaluation of Bridges Considering Aspect Ratio of Pier in Near-Fault and Far-Fault Ground Motions. *Applied Sciences*. 2020; 10(17):6098.
https://doi.org/10.3390/app10176098

**Chicago/Turabian Style**

An, Hyojoon, Jong-Han Lee, and Soobong Shin.
2020. "Dynamic Response Evaluation of Bridges Considering Aspect Ratio of Pier in Near-Fault and Far-Fault Ground Motions" *Applied Sciences* 10, no. 17: 6098.
https://doi.org/10.3390/app10176098