# Seismic Analysis of a Curved Bridge Considering Soil-Structure Interactions Based on a Separated Foundation Model

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## Abstract

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## 1. Introduction

## 2. Wave Input Calculation Model

## 3. Free-Field One-Dimensional Time Domain Algorithm Based on the Mass Method

^{5}of the total mass), and the corresponding seismic excitation equivalent load is $\mathit{P}(t)={\mathit{M}}_{m,N}{\ddot{\mathit{u}}}_{g}(t)$. This will generate additional damping force for large mass points when considering Rayleigh damping, resulting in a smaller calculation result [26]. Therefore, the damping force at the large mass point is omitted in the dynamic equations to improve the accuracy of the mass method. Further, according to Equation (3), the motion equation of the node of the mth column can be obtained as follows:

## 4. Free-Field Displacement Extension Solution

## 5. Near-Field Foundation-Bridge Model and Numerical Verification

## 6. Synthesis of Multisupport-Related Ground Motion

## 7. Analytical Method Based on the Separated Foundation Model

## 8. Seismic Response Analysis of the Curved Beam Bridge

#### 8.1. Project Overview

#### 8.2. Separated Foundation-Bridge System Finite Element Model

#### 8.3. Generation of Seismic Coherent Waves

#### 8.4. Effect of Different Apparent Wave Velocities on the Structural Response

_{z}of the beam is more sensitive to changes in the apparent wave velocity and that it increases as the apparent wave velocity decreases. Wave passage has little effect on the bending moment at the bottom of the pier.

#### 8.5. Effect of Different Coherence on the Structural Response

#### 8.6. Effect of Different Site Conditions on the Structural Response

## 9. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 7.**Direct solution model (

**Left**) and the substructure model (near-field.foundation-bridge model) (

**Right**).

**Figure 14.**Internal force responses of the beam and the bottom of the pier for different apparent wave velocities.

**Figure 15.**Internal force response of the beam and the bottom of the pier under different values of coherence.

**Figure 16.**Internal force response of the beam and the bottom of the pier under different site conditions.

Working Condition | Shear Wave Velocity (m/s) | Apparent Wave Velocity (m/s) | Coherence | ||||
---|---|---|---|---|---|---|---|

P1 | P2 | P3 | P4 | P5 | |||

1 | The soil parameters are consistent with those described in the project overview. | 390 | s = 1000 | ||||

2 | 650 | s = 1000 | |||||

3 | 910 | s = 1000 | |||||

4 | 1300 | s = 1000 | |||||

5 | $+\infty $ | s = 1000 | |||||

6 | $+\infty $ | s = 10 | |||||

7 | $+\infty $ | s = 1 | |||||

8 | $+\infty $ | s = 0.1 | |||||

9 | 150 | 150 | 150 | 150 | 150 | $+\infty $ | s = 1000 |

10 | 300 | 300 | 300 | 300 | 300 | $+\infty $ | s = 1000 |

11 | 450 | 450 | 450 | 450 | 450 | $+\infty $ | s = 1000 |

12 | 300 | 150 | 150 | 150 | 150 | $+\infty $ | s = 1000 |

13 | 300 | 300 | 300 | 150 | 150 | $+\infty $ | s = 1000 |

^{3}.

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**MDPI and ACS Style**

Zhang, L.; Gu, Y.
Seismic Analysis of a Curved Bridge Considering Soil-Structure Interactions Based on a Separated Foundation Model. *Appl. Sci.* **2020**, *10*, 4260.
https://doi.org/10.3390/app10124260

**AMA Style**

Zhang L, Gu Y.
Seismic Analysis of a Curved Bridge Considering Soil-Structure Interactions Based on a Separated Foundation Model. *Applied Sciences*. 2020; 10(12):4260.
https://doi.org/10.3390/app10124260

**Chicago/Turabian Style**

Zhang, Lixin, and Yin Gu.
2020. "Seismic Analysis of a Curved Bridge Considering Soil-Structure Interactions Based on a Separated Foundation Model" *Applied Sciences* 10, no. 12: 4260.
https://doi.org/10.3390/app10124260