# Dynamic Response Mechanism of Silt Ground under Vibration Load

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Model Parameter Selection

#### 2.2. The Establishment of Computational Model

#### 2.3. Boundary Conditions

#### 2.4. Damping Parameters

_{1}and L

_{2}are the two parameters of the default model, and L

_{1}= −3.156, L

_{2}= 1.904 [24].

#### 2.5. Dynamic Load Input

#### 2.6. Distribution of Monitoring Points

## 3. Results and Analysis

#### 3.1. Dynamic Response Analysis of One-Way Train Running

^{2}, 5.12 m/s

^{2}, and 7.20 m/s

^{2}, respectively. Under the same speed and the same action time, the acceleration peak value of each monitoring point also gradually decreased with the increase in the horizontal distance. The greater the speed of the train, the greater the magnitude of the ground acceleration response.

^{2}, 7.40 m/s

^{2}, and 10.35 m/s

^{2}, respectively.

#### 3.2. Dynamic Response Analysis of Two-Way Trains in Operation

^{2}. When the speed of the train was 54 km/h, the maximum acceleration response was 6.10 m/s

^{2}. When the speed of the train was 90 km/h, the maximum acceleration response was 7.89 m/s

^{2}. The peak value of the acceleration time-history curve increases as the speed of the subway train increases. Under the same speed and the same action time, the peak value of the acceleration time-history curve decreases as the horizontal distance increases.

^{2}, 8.40 m/s

^{2}, and 26 m/s

^{2}, respectively. When the train running speed was 90 km/h, the peak value of the acceleration time-history curve caused by the dynamic load of the two-way train is twice that of the one-way train.

## 4. Conclusions

- (1)
- Under the action of train dynamic load, the stratum around the tunnel will produce vibration subsidence. When the subway train runs in one direction, the maximum vibration-sag caused by the train at the speed of 30 km/h, 54 km/h, and 90 km/h is 1.02 cm, 1.59 cm, and 2.79 cm, respectively. When the subway train runs in two directions, the maximum vibration-sag caused by the train at the speed of 30 km/h, 54 km/h, and 90 km/h is 1.04 cm, 1.62 cm, and 2.95 cm, respectively.
- (2)
- Under the action of train dynamic load, from the change trend of the displacement time-history curve, it can be seen that with the increase in train speed, the peak value of the displacement time-history curve also increases. With the increase in horizontal distance between surface monitoring points and vibration sources, the peak value of the displacement time-history curve decreases. When the speed of monitoring point B above the vibration source is 30 km/h, 54 km/h, and 90 km/h, the maximum vertical displacement caused by one-way running of the train is 0.76 mm, 1.52 mm, and 1.84 mm, respectively. The maximum vertical displacements caused by two-way running are 1.04 mm, 1.88 mm, and 2.28 mm, respectively. Compared with one-way train dynamic load, the vertical displacement caused by two-way train dynamic load is much larger.
- (3)
- Under the action of train vibration load, the acceleration response of the stratum around the tunnel lags behind. From the change trend of the acceleration time-history curve, it can be seen that acceleration response will be delayed for a period of time. When the train speed is 30 km/h, 54 km/h, and 90 km/h, the acceleration peaks are 2.59 m/s
^{2}, 5.12 m/s^{2}, and 7.20 m/s^{2}, respectively. The acceleration peaks of trains passing through the tunnel in two directions are 3.30 m/s^{2}, 6.10 m/s^{2}, and 7.89 m/s^{2}, respectively. The faster the train runs, the greater the peak value of the acceleration time-history curve. The peak value of the acceleration time-history curve under bidirectional train vibration load is larger than that under unidirectional train vibration load. However, with the passage of time, the peak value of the acceleration time-history curve is gradually attenuating. Under the condition of the same speed and the same action time, the peak value of the acceleration time-history curve decreases with the increase in horizontal distance from the vibration source. - (4)
- There is a lack of long-term measured data in the simulation of train dynamic load. This may result in the difference between the simulation and the real situation. This is the problem that needs to be solved in a future study.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**Displacement time-history curve and acceleration time-history curve of surface monitoring point of one-way train running.

**Figure 7.**Displacement time-history curve and acceleration time-history curve of monitoring point at tunnel interlayer of one-way train running.

**Figure 9.**Displacement time-history curve and acceleration time-history curve of surface monitoring point of two-way train running.

**Figure 10.**Displacement time-history curve and acceleration time-history curve of monitoring point at tunnel interlayer of two-way train running.

No. | Soil Layer | Thickness /m | $\mathit{\gamma}$/ (kN/m ^{3}) | $\mathit{c}$/ kPa | $\mathit{\phi}$/ $(\xb0)$ | $\mathit{E}\mathit{s}/$ MPa | $\mathit{\mu}$ |
---|---|---|---|---|---|---|---|

1 | Fill | 2.00 | 18.50 | 20.00 | 9.00 | 5.77 | 0.30 |

2 | Silty clay | 5.00 | 19.70 | 27.50 | 23.00 | 17.55 | 0.30 |

3 | Silt-1 | 5.00 | 20.00 | 18.00 | 32.00 | 18.00 | 0.30 |

4 | Silt-2 | 36.00 | 10.00 | 18.00 | 32.00 | 18.00 | 0.30 |

No. | Soil Layer | Elastic Modulus /MPa | Poisson’s Ratio $\mathit{\mu}$ | Volume Modulus $\mathit{K}$/MPa | Shear Modulus $\mathit{G}$/MPa | $\mathit{\gamma}$ (kN/m ^{3}) |
---|---|---|---|---|---|---|

1 | fill | 5.77 | 0.30 | 4.81 | 2.22 | 18.50 |

2 | Silty clay | 17.55 | 0.30 | 14.63 | 6.75 | 19.70 |

3 | silt-1 | 18.00 | 0.30 | 15.00 | 6.92 | 20.00 |

4 | silt-2 | 18.00 | 0.30 | 15.00 | 6.92 | 10.00 |

5 | lining | 34,500.00 | 0.30 | 19,166.67 | 14,375.00 | 25.00 |

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**MDPI and ACS Style**

Gu, Z.; Wei, H.; Liu, Z.; Zhang, M.
Dynamic Response Mechanism of Silt Ground under Vibration Load. *Sustainability* **2022**, *14*, 10335.
https://doi.org/10.3390/su141610335

**AMA Style**

Gu Z, Wei H, Liu Z, Zhang M.
Dynamic Response Mechanism of Silt Ground under Vibration Load. *Sustainability*. 2022; 14(16):10335.
https://doi.org/10.3390/su141610335

**Chicago/Turabian Style**

Gu, Zhanfei, Hailong Wei, Zhikui Liu, and Mingfei Zhang.
2022. "Dynamic Response Mechanism of Silt Ground under Vibration Load" *Sustainability* 14, no. 16: 10335.
https://doi.org/10.3390/su141610335