# Building Vibration Measurement and Prediction during Train Operations

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Field Measurement

#### 2.1. Measurement Setup

^{2}. The building foundation is a rigid foundation with a base size of 1.2 × 1.2 m

^{2}. Table 2 lists the dimensions and dynamics parameters of the building structure, where h, t,

**w**, E, and ρ are the height, thickness, width, elastic modulus, density of the structural components, respectively. The damping ratio and Poisson’s ratio of the reinforced concrete structural components are 0.02 and 0.2, respectively.

#### 2.2. Measurement Results

^{2}is greater than the column vibration with a peak acceleration of about 0.008 m/s

^{2}.

## 3. Vibration Prediction and Validation

#### 3.1. Prediction Model

#### 3.1.1. Soil–Structure Interaction Model

#### 3.1.2. Building Model

#### 3.1.3. System Assembly

#### 3.2. Model Validation

#### 3.2.1. Transmission Ratio from Soil to Structure

#### 3.2.2. Building Vibration

## 4. Discussion

## 5. Conclusions

- (1)
- The predicted vibration is in good agreement with the measured vibration, and the established prediction model can reasonably predict the vibration of a building with a rigid foundation caused by train operation once the ground vibration can be obtained via measurement.
- (2)
- The coupling loss is obvious as the vibration propagates from the soil to the rigid foundation, and the vibration tends to decrease significantly with an increase in frequency.
- (3)
- For s rigid building foundation, the coupling effect of soil and structure causes a low-frequency building–soil resonance and a high-frequency amplitude attenuation. This effect becomes more pronounced with higher building heights, leading to a more significant change in high-frequency amplitude.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Measured acceleration levels of a 1/3 octave band frequency. (

**a**) Comparison of ground vibration and column vibration on 1st floor; (

**b**) comparison of floor vibration on 1st floor and 2nd floor.

**Figure 7.**Comparison of measured vibration and predicted vibration from soil to column. (

**a**) Transmission ratio; (

**b**) column vibration on 1st floor.

**Figure 8.**Comparison of measured vibration and predicted vibration within the building (

**a**) at the column; (

**b**) at the floor center.

**Figure 10.**Difference between each floor vibration inside the building and ground vibration. (

**a**) Two-story building; (

**b**) five-story building; (

**c**) eight-story building.

Name | Thickness (m) | Density (kg/m^{3}) | Poisson’s Ratio | Modulus of Elasticity (MPa) |
---|---|---|---|---|

Plain fill | 2.1 | 16 | 0.45 | 120 |

Clay | 1.3 | 18.4 | 0.46 | 130 |

Muck | 8.4 | 17.5 | 0.48 | 300 |

Silty clay | 10.6 | 19.3 | 0.45 | 380 |

Structural Component | h (m) | t (m) | w (m) | E (Gpa) | ρ (kg/m^{3}) |
---|---|---|---|---|---|

Column | 4 | 0.4 | 0.4 | 32.5 | 2500 |

Floor slab | - | 0.1 | - | 30 | 2500 |

Rigid foundation | - | 1.2 | 1.2 | 32.5 | 2500 |

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**MDPI and ACS Style**

He, L.; Tao, Z.
Building Vibration Measurement and Prediction during Train Operations. *Buildings* **2024**, *14*, 142.
https://doi.org/10.3390/buildings14010142

**AMA Style**

He L, Tao Z.
Building Vibration Measurement and Prediction during Train Operations. *Buildings*. 2024; 14(1):142.
https://doi.org/10.3390/buildings14010142

**Chicago/Turabian Style**

He, Lingshan, and Ziyu Tao.
2024. "Building Vibration Measurement and Prediction during Train Operations" *Buildings* 14, no. 1: 142.
https://doi.org/10.3390/buildings14010142