# Study on the Stability and Seepage Characteristics of Underwater Shield Tunnels under High Water Pressure Seepage

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Method and Numerical Models

#### 2.1. Basic Principles of Fluid–Solid Coupling

#### 2.1.1. Stress Balance Equation

#### 2.1.2. Seepage Continuity Equation

#### 2.1.3. Theoretical Derivation of an Anisotropic Permeability Coefficient Expression

#### 2.2. Numerical Modeling

#### 2.2.1. Modeling Assumptions

- (1)
- The solid units of the model follow the Mohr–Coulomb yield criterion;
- (2)
- The properties of the soil and structural units do not change during excavation, and the soil particles and fluids are incompressible;
- (3)
- The geotechnical body is regarded as a porous medium, and the flow of fluid in the pores conforms to Darcy’s law;
- (4)
- The shield shell and lining units are considered to be perfectly elastic, and both are impermeable.

#### 2.2.2. Engineering Background

#### 2.2.3. Modeling

#### 2.2.4. Calculation Parameters

^{3}, Poisson’s ratio is 0.3, modulus of elasticity is 34.5 GPa, stiffness reduction coefficient is 0.8, and shell unit is adopted; the shield shell of shield machine has a density of 7850 kg/m

^{3}, Poisson’s ratio is 0.2, modulus of elasticity is 210 GPa, and liner unit is adopted; a homogeneous and equal-thickness “equivalent layer” is adopted to simulate the grouting process, and the slurry hardening process is simplified. To simulate the grouting process and simplify the hardening process of the slurry, within 2.4 m of the shield tail is the flowing equivalent layer, with a thickness of 0.06 m, density of 2000 kg/m

^{3}, elastic modulus of 0.75 MPa, Poisson’s ratio of 0.35, and outside the 2.4 m of the shield tail is the initial condensation equivalent layer, with a thickness of 0.06 m, density of 2300 kg/m

^{3}, elastic modulus of 10 MPa, elastic modulus of 0.2, and equivalent layer of 10 MPa. The density is 2300 kg/m

^{3}, the modulus of elasticity is 10 MPa, and Poisson’s ratio is 0.25. According to the geological investigation report, the physicomechanical parameters of each layer of the soil body are shown in Table 1.

#### 2.2.5. Simulation Process

#### 2.3. Boundary Conditions and Initial Conditions

^{4}Pa applied to the upper surface of the model; the front, back, left, and proper four characters of the model are set as horizontal displacement constraints; the displacement of the bottom surface is a fixed constraint.

^{4}Pa is applied on the upper surface of the model. For soft clay, its permeability coefficient is small. In the transient deformation stage of shield tunnel construction, the external boundary of the model is not as good as the drainage, so it is assumed that other limitations, including the front and rear borders of the model, the left and right boundaries, the bottom boundary, and the boundary of the tunnel, in addition to the upper surface, are impervious. In the long-term development and change process of tunnel consolidation and settlement, the pore water pressure should be kept as the initial hydrostatic pressure value due to the model front and rear boundaries, left and right borders, and bottom boundaries being far away from the tunnel. Hence, the model front and rear edges, left and proper limits, and bottom boundaries are infiltrated. The pore water pressure inside the border of the segment is fixed at 0 during the tunnel shield excavation process.

## 3. Results and Discussions

#### 3.1. Analysis of Displacement Field

**Figure 4.**Vertical displacement distribution of monitoring section A. (

**a**) Distribution of the left tunnel after excavation and penetration; (

**b**) distribution of the right tunnel after excavation and penetration; (

**c**) vertical deformation curve of the strata after excavation and penetration of the left tunnel; (

**d**) vertical deformation curve of the strata after excavation and penetration of the right tunnel.

#### 3.2. Analysis of Seepage Field

#### 3.3. Analysis of Key Construction Parameters

#### 3.4. Seepage Characteristics of Shield Tunnel under High Water Pressure

#### 3.4.1. Distribution Law of Seepage Field of Surrounding Rock

#### 3.4.2. Surface Settlement

## 4. Conclusions

- (1)
- After shield excavation, the late consolidation settlement of the soil under seepage is enormous, accounting for about 25% of the total settlement, and the later tunnel will further enhance the seepage around the first tunnel.
- (2)
- During the construction of the underwater shield, the pore water pressure on both sides of the tunnel arch and arch waist is reduced by about 72% and 30%, respectively, compared with the initial value and requiring focused monitoring of the tunnel arch girdle area.
- (3)
- Within a specific range, increasing the digging pressure and grouting pressure and reducing the thickness of the grouting layer can effectively control the vertical deformation of the segment, and reducing the grouting stress and thickness of the grouting layer can effectively prevent the horizontal deformation of the segment.
- (4)
- The more prominent the overlying water level is, the more pronounced the seepage effect is, and the larger the maximum consolidation settlement and the influence range of the surface settlement. The influence of the water level on the force of the segment should be considered in the structural design of the segment.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 7.**Cloud diagram of seepage field distribution in monitoring section A. (

**a**) After the left tunnel is excavated through; (

**b**) after the right tunnel is excavated through.

**Figure 8.**Deformation curves of the segment of the shield tunnel in the left line of monitoring section A under different tunneling pressures. (

**a**) Vertical deformation; (

**b**) horizontal deformation.

**Figure 9.**Deformation curves of the segment of the shield tunnel in the left line of monitoring section A under different grouting pressures. (

**a**) Vertical deformation; (

**b**) horizontal deformation.

**Figure 10.**Deformation curve of the segment of the left line shield tunnel in monitoring section A under different thicknesses of grouting layer. (

**a**) Vertical deformation; (

**b**) horizontal deformation.

**Figure 11.**Pore water pressure distribution in the tunnel surroundings after asynchronous tunnel excavation and penetration of the two-lane tunnel under different overlying water level conditions. (

**a**) Overlying water depth 10 m; (

**b**) overlying water depth 20 m; (

**c**) overlying water depth 30 m; (

**d**) overlying water depth 40 m.

Floor Number | Thickness (m) | Porosity | Permeability Coefficient (cm·s^{−1}) | Specific Weight (kN/m ^{3}) | Elastic Modules (MPa) | Cohesion (kPa) | Poisson’s Ratio | Friction Angle (°) | |
---|---|---|---|---|---|---|---|---|---|

Vertical | Level | ||||||||

2-4 | 3.1 | 0.386 | 2.69 × 10^{−4} | 6.37 × 10^{−4} | 20 | 12 | 6.78 | 0.25 | 35.8 |

2-3-1 | 7.1 | 0.418 | 1.72 × 10^{−6} | 2.91 × 10^{−6} | 19.7 | 9.3 | 10.9 | 0.31 | 17.9 |

2-2-1 | 2.2 | 0.456 | 1.65 × 10^{−7} | 2.72 × 10^{−7} | 19.3 | 11.5 | 22.2 | 0.34 | 10.7 |

2-4 | 8.7 | 0.386 | 2.69 × 10^{−4} | 6.37 × 10^{−4} | 20 | 12 | 6.78 | 0.25 | 35.8 |

2-5 | 10.5 | 0.363 | 8.01 × 10^{−4} | 1.89 × 10^{−3} | 20.4 | 10 | 8.53 | 0.29 | 35.9 |

2-3-3 | 6.7 | 0.418 | 1.55 × 10^{−6} | 2.34 × 10^{−6} | 19.8 | 7.6 | 11.6 | 0.3 | 14.7 |

3-6 | 7.7 | 0.319 | 9.61 × 10^{−4} | 2.26 × 10^{−3} | 20.4 | 10.03 | 13.6 | 0.28 | 32.58 |

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**MDPI and ACS Style**

Chen, L.; Xi, B.; Dong, Y.; He, S.; Shi, Y.; Gao, Q.; Liu, K.; Zhao, N.
Study on the Stability and Seepage Characteristics of Underwater Shield Tunnels under High Water Pressure Seepage. *Sustainability* **2023**, *15*, 15581.
https://doi.org/10.3390/su152115581

**AMA Style**

Chen L, Xi B, Dong Y, He S, Shi Y, Gao Q, Liu K, Zhao N.
Study on the Stability and Seepage Characteristics of Underwater Shield Tunnels under High Water Pressure Seepage. *Sustainability*. 2023; 15(21):15581.
https://doi.org/10.3390/su152115581

**Chicago/Turabian Style**

Chen, Luhai, Baoping Xi, Yunsheng Dong, Shuixin He, Yongxiang Shi, Qibo Gao, Keliu Liu, and Na Zhao.
2023. "Study on the Stability and Seepage Characteristics of Underwater Shield Tunnels under High Water Pressure Seepage" *Sustainability* 15, no. 21: 15581.
https://doi.org/10.3390/su152115581