# Foundation Settlement Response of Existing High-Speed Railway Bridge Induced by Construction of Undercrossing Roads

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Overview of Study Area

#### 2.1. Project Overview

#### 2.2. Hydrogeological Overview

## 3. Theory of Pile-Soil Interaction

#### 3.1. Analysis of Soil Displacement Caused by Pit Excavation

#### 3.2. Analysis of Pile-Soil Interaction Induced by Foundation Excavation

_{s}is the thickness of the laterally displaced soil layer, h

_{p}is the length of the pile adjacent to the pit excavation, and $\lambda $ is the relative stiffness of the pile and soil. The relative stiffness of the pile and soil can be calculated by the following equations:

_{h}is the horizontal foundation reaction coefficient, E

_{p}is the modulus of elasticity of the adjacent pile, and I

_{p}is the moment of inertia of the adjacent pile. It is difficult to directly solve the special solution of Equation (3). Thus, a polynomial is used to approximate the soil displacement distribution function, which can be calculated by the following equations:

## 4. Numerical Simulation

#### 4.1. Calculation Model and Parameters Setting

^{−1}with a friction coefficient of 0.3.

#### 4.2. Boundary and Calculation Settings of the Model

#### 4.3. Monitoring Results and Validation of Numerical Simulation Model

#### 4.4. Ground Surface Settlement

#### 4.5. Surface Displacement of Soil Layers between Pits

#### 4.6. Deformation Analysis of Bridge Pile

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$\Delta $ | Empirical formula for ground settlement |

$d$ | The clear distance from the edge of the pit |

$H$ | The depth of pit excavation |

$s(x,z),s(z),s$ | Equation for the lateral displacement of the free field soil |

$(x,z)$ | Any point of the free field soil outside the foundation pit |

$f(\xi )$ | The fitted curve function of the horizontal displacement of a support pile |

$\xi $ | The integral variable |

L | The depth of the support pile |

$v$ | Pile deflection |

h_{s} | Thickness of the laterally displaced soil layer |

h_{p} | Length of the pile adjacent to the pit excavation |

$\lambda $ | Relative stiffness of pile and soil |

k | Deformation force per unit volume of soil within each width of the pile |

k_{h} | Horizontal foundation reaction coefficient |

E_{p} | Modulus of elasticity of the adjacent pile |

I_{p} | Moment of inertia of the adjacent pile |

a_{i}, b_{j} | The constant coefficients |

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**Figure 4.**The 3D finite difference model of new roads undercrossing an existing high-speed railway bridge. (

**a**) The overall model; (

**b**) the pile model.

**Figure 6.**Comparison of monitoring data and numerical simulation results of bridge piers’ vertical displacement: (

**a**) monitoring data; (

**b**) numerical simulation results.

**Figure 7.**Surface settlement contours of the construction of undercrossing roads under different steps (unit: mm): (

**a**) Step 1; (

**b**) Step 2; (

**c**) Step 3; (

**d**) Step 4; (

**e**) Step 5; (

**f**) Step 6.

**Figure 8.**Surface displacement of the left side soil layers between pits under different steps: (

**a**) Step 1; (

**b**) Step 2; (

**c**) Step 3; (

**d**) Step 4; (

**e**) Step 5; (

**f**) Step 6.

**Figure 9.**Surface displacement of the right side soil layers between pits under different steps: (

**a**) Step 1; (

**b**) Step 2; (

**c**) Step 3; (

**d**) Step 4; (

**e**) Step 5; (

**f**) Step 6.

**Figure 10.**Numerical simulation monitoring position of surface displacement of the soil layers between pits.

**Figure 11.**Vertical and horizontal displacement of piles of high-speed railway bridge piers under different steps. (

**a**) piles of the pier 251; (

**b**) piles of the pier 251; (

**c**) piles of the pier 252; (

**d**) piles of the pier 252.

**Figure 12.**Axial stress of piles of high-speed railway bridge piers under different steps. (

**a**) piles of the pier 251; (

**b**) piles of the pier 252; (

**c**) piles of the pier 253; (

**d**) piles of the pier 254.

Layer Number | Type | Thickness (m) | Weight (kN/m^{3}) | Poisson’s Ratio | Bulk (MPa) | Shear (MPa) | Cohesion (kPa) | Fric (°) |
---|---|---|---|---|---|---|---|---|

1 | Silty soil | 4 | 18 | 0.3 | 23.33 | 10.77 | 10 | 20 |

2 | Silty sand | 2 | 18 | 0.35 | 36.28 | 12.09 | 2 | 30 |

3 | Silty clay | 1 | 18 | 0.3 | 12.17 | 5.62 | 10 | 20 |

4 | Silty sand | 2 | 18 | 0.35 | 36.28 | 12.09 | 2 | 30 |

5 | Medium sand | 5 | 18 | 0.35 | 61.11 | 20.37 | 3 | 30 |

Bridge | C50 | - | 25 | 0.2 | 19,166.67 | 14,375 | - | - |

Pier | C30 | 60 | 25 | 0.2 | 16,666.67 | 12,500 | - | - |

Bridge base | C30 | 2.5 | 25 | 0.2 | 16,666.67 | 12,500 | - | - |

Pile of the bridge | C35 | 42 | 25 | 0.2 | 17,500 | 13,125 | - | - |

Pavement of the new roads | Asphalt concrete | 0.35 | 24.5 | 0.35 | 1666.67 | 555.56 | - | - |

The u-shaped groove structure | C35 | 0.5 | 25 | 0.2 | 17,500 | 13,125 | - | - |

Beam of the new roads | C35 | 0.5 | 25 | 0.2 | 17,500 | 13,125 | - | - |

Pile of the new roads | C25 | 13 | 25 | 0.2 | 15,555.56 | 11,666.67 | - | - |

Serial Number | Construction Sequence | Step |
---|---|---|

1 | Excavation of the road foundation pits | Step 1 |

2 | Drilling of the road piles | Step 2 |

3 | Grouting of the road piles | Step 3 |

4 | Pouring of the road beams | Step 4 |

5 | Pouring of the u-shaped plates | Step 5 |

6 | Paving of the road surfaces | Step 6 |

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**MDPI and ACS Style**

Wang, Y.; Liang, S.; Huang, C.; Wang, R.
Foundation Settlement Response of Existing High-Speed Railway Bridge Induced by Construction of Undercrossing Roads. *Sustainability* **2022**, *14*, 8700.
https://doi.org/10.3390/su14148700

**AMA Style**

Wang Y, Liang S, Huang C, Wang R.
Foundation Settlement Response of Existing High-Speed Railway Bridge Induced by Construction of Undercrossing Roads. *Sustainability*. 2022; 14(14):8700.
https://doi.org/10.3390/su14148700

**Chicago/Turabian Style**

Wang, You, Shaohua Liang, Changxi Huang, and Rui Wang.
2022. "Foundation Settlement Response of Existing High-Speed Railway Bridge Induced by Construction of Undercrossing Roads" *Sustainability* 14, no. 14: 8700.
https://doi.org/10.3390/su14148700