# Experimental Study on Vibration Velocity of Piled Raft Supported Embankment and Foundation for Ballastless High Speed Railway

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experiment Overview

#### 2.1. Experimental Model

#### 2.2. Applied Dynamic Load

## 3. Results and Discussions

#### 3.1. Analysis of Vibration Velocities in Time and Frequency Domain

#### 3.2. Distribution of Vibration Velocities in Piled Raft Foundation

#### 3.3. Influence of Train Speeds

## 4. Conclusions

- (1)
- The time history and peak vibration velocity of the track structure, roadbed, embankment, and piled raft foundation are clearly visible and have sharp impulse and relaxation patterns, corresponding to the loading of train wheels, bogies, and passages. Vibration velocity at the track slab is much stronger than that at roadbed, and sharply decreases when transmitting from track slab to roadbed, reducing by nearly 90%, comes to about 98% at the subsoil surface.
- (2)
- Most of the frequency contents of vibration velocity at various locations are mainly concentrated at harmonic frequencies of 2 Hz, 4 Hz, 6 Hz, 8 Hz, 12 Hz, 18 Hz, 20 Hz for the train speed of 180 km/h, of which the frequency 2 Hz, 6 Hz, and 20 Hz correspond to one carriage length of 25 m, the adjacent bogie spacing of 7.5 m and two wheels spacing of 2.5 m. The change of water level has slight impac on the peak spectrum of vibration velocity at harmonic frequencies.
- (3)
- The vibration velocity levels inside the embankment and subsoil are lower than those on the surface of the track structure and embankment, but still have visible impulse. Vibration velocities decrease quickly in the roadbed and embankment, and then the decreasing rates slow down. With the increase of soil depth, the differences of dynamic velocities in subsoils between different locations become smaller and have very low values.
- (4)
- The dynamic responses of track slab, roadbed, embankment, piled raft, and subsoils are dominated by the dimensions of trains, properties of vibration medium, and load excitation sources. The vibration absorption and attenuation of the embankment and piled raft structure also influence the vibration load transmission and attenuation. The train speeds have more impact on the vibration attenuation in both track structure and substructure.
- (5)
- The vibration velocity attenuations mainly follow the distribution law of exponential curve at different train speed, which can give some empirical guidance for further prediction and analysis on the vibration velocity response of ballastless slab track, embankment, and piled raft supported foundations. The piled raft structure will produce a resistance and excitation effect on the vibration of upper embankment materials.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Geometry configuration of the high-speed trains and M-shaped wave. (

**a**) Geometry configuration of the high-speed trains; (

**b**) M-shaped wave.

**Figure 4.**Loading curves at reduced scale for train speed of 180 km/h and 270 km/h in time and frequency domain. (

**a**) time domain; (

**b**) frequency domain.

**Figure 5.**Time histories of vibration velocity at track slab V2, roadbed V3, and subsoil surface V6. (

**a**) Low water level v = 180 km/h, (

**b**) High water level, v = 180 km/h.

**Figure 6.**Time histories of velocity at track slab V2, roadbed V3, and subsoil surface V6. (

**a**) Low water level, v = 270 km/h, (

**b**) High water level, v = 270 km/h.

**Figure 7.**Frequency contents of velocity at track V2, V3, V6. (

**a**) Low water level, v = 180 km/h, (

**b**) High water level, v = 180 km/h.

**Figure 8.**Frequency contents of velocity at track V2, V3, V6. (

**a**) Low water level, v = 270 km/h, (

**b**) High water level, v = 270 km/h.

**Figure 9.**Time histories of vibration velocities at embankment top V7, raft top V8, and subsoil top V9. (

**a**) Low water level v = 180 km/h, (

**b**) High water level, v = 180 km/h.

**Figure 10.**Time histories of vibration velocities at embankment top V7, raft top V8, and subsoil top V9. (

**a**) Low water level v = 270 km/h, (

**b**) High water level, v = 270 km/h.

**Figure 11.**Frequency contents of vibration velocities at embankment top V7, raft top V8, and subsoil top V9. (

**a**) Low water level, (

**b**) High water level, v = 180 km/h.

**Figure 12.**Frequency contents of vibration velocities at embankment top V7, raft top V8, and subsoil top V9. (

**a**) Low water level, (

**b**) High water level, v = 270 km/h.

**Figure 13.**Vibration velocity distribution in horizontal direction from the track center. (

**a**) low water level, (

**b**) high water level.

**Figure 14.**Fitting curves of peak velocity in horizontal direction along with distance from the track center. (

**a**) Low water level, (

**b**) High water level.

**Figure 15.**Vibration velocity distribution in vertical direction along the depth from roadbed. (

**a**) low water level, (

**b**) high water level.

**Figure 16.**Relationship between vibration velocities and train speed at V3 to V6. (

**a**) low water level, (

**b**) high water level.

**Figure 17.**Relationship between vibration velocities and train speed at V7 to V11. (

**a**) low water level (

**b**) high water level.

Parameters | Scale Factors | Parameters | Scale Factors |
---|---|---|---|

Load | 1:25 | velocity | 1 |

stress | 1 | time | 1:5 |

volume | 1:125 | length | 1:5 |

frequency | 5 | modulus | 1 |

density | 1 |

Model | ExpDec1 | |||||
---|---|---|---|---|---|---|

Equation | y = A1exp(−x/t1) + y0 | |||||

Train speed | v = 90 km/h | v = 180 km/h | v = 270 km/h | |||

Water level | LWL | HWL | LWL | HWL | LWL | HWL |

y0 | 0.38 | 0.078 | 1.24 | 0.525 | 1.75 | 0.744 |

A1 | 238 | 51 | 687 | 128 | 2619 | 134 |

t1 | 0.079 | 0.178 | 0.075 | 0.151 | 0.058 | 0.196 |

Reduced Chi-Sqr | 0.129 | 4.55 | 1.113 | 11.23 | 1.141 | 58.6 |

RSquare (COD) | 0.9966 | 0.92 | 0.9953 | 0.947 | 0.9978 | 0.883 |

Adjusted RSquare | 0.9933 | 0.841 | 0.9906 | 0.895 | 0.9957 | 0.766 |

Train Speed | v = 90 km/h | v = 180 km/h | v = 270 km/h | |||
---|---|---|---|---|---|---|

Water Level | LWL | HWL | LWL | HWL | LWL | HWL |

Locations | Percent | Percent | Percent | Percent | Percent | Percent |

V2 | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% |

V3 | 88.83% | 90.30% | 88.65% | 89.13% | 92.28% | 88.86% |

V4 | 92.37% | 92.54% | 91.24% | 90.61% | 93.97% | 91.55% |

V5 | 97.12% | 95.00% | 94.85% | 91.57% | 93.52% | 87.72% |

V6 | 99.24% | 99.38% | 99.42% | 97.89% | 98.62% | 98.06% |

Train Speed | v = 90 km/h | v = 180 km/h | v = 270 km/h | |||
---|---|---|---|---|---|---|

Water Level | LWL | HWL | LWL | HWL | LWL | HWL |

Locations | Percent | Percent | Percent | Percent | Percent | Percent |

V7 | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% |

V8 | 63.01% | 66.53% | 42.25% | 48.06% | −38.11% | 11.85% |

V9 | 80.08% | 84.38% | 80.33% | 73.42% | 70.86% | 55.40% |

V10 | 91.75% | 92.25% | 90.28% | 88.34% | 73.25% | 90.68% |

V11 | 96.75% | 94.73% | 91.06% | 92.48% | 76.02% | 92.65% |

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**MDPI and ACS Style**

Fu, Q.; Gu, M.; Yuan, J.; Lin, Y.
Experimental Study on Vibration Velocity of Piled Raft Supported Embankment and Foundation for Ballastless High Speed Railway. *Buildings* **2022**, *12*, 1982.
https://doi.org/10.3390/buildings12111982

**AMA Style**

Fu Q, Gu M, Yuan J, Lin Y.
Experimental Study on Vibration Velocity of Piled Raft Supported Embankment and Foundation for Ballastless High Speed Railway. *Buildings*. 2022; 12(11):1982.
https://doi.org/10.3390/buildings12111982

**Chicago/Turabian Style**

Fu, Qiang, Meixiang Gu, Jie Yuan, and Yifeng Lin.
2022. "Experimental Study on Vibration Velocity of Piled Raft Supported Embankment and Foundation for Ballastless High Speed Railway" *Buildings* 12, no. 11: 1982.
https://doi.org/10.3390/buildings12111982