# The Unsymmetrical Coefficient of Unsymmetrical-Loaded Tunnel Based on Field Monitoring and Numerical Simulation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Field Test

#### 2.1. Engineering Background

#### 2.2. Monitoring Arrangement

#### 2.3. Monitoring Results

#### 2.3.1. Pressure between the Surrounding Rock and Primary Support

#### 2.3.2. Pressure between the Primary Support and Second Lining

#### 2.3.3. Strain of the Second Lining

## 3. Unsymmetrical Coefficient and Application

#### 3.1. Unsymmetrical Coefficient

#### 3.2. Application in HTG Tunnel

#### 3.2.1. Numerical Model

_{0}is the elastic modulus of jet concrete, in MPa; E

_{g}is the elastic modulus of the steel arch, in MPa; S

_{g}is the cross-sectional area of the steel arch, in m

^{2}; and S

_{c}is the cross-sectional area of jet concrete in m

^{2}.

#### 3.2.2. Simulation Results

- (1)
- Distribution of the Stress and Strain

- (2)
- Comparation of Unsymmetrical Coefficient

## 4. Single Factor Analysis

#### 4.1. Influence of Topographic Factors

#### 4.1.1. Impact of Slope Angle

#### 4.1.2. Influence of the Cover Thickness

#### 4.2. Effects of the Surrounding Rock Properties

#### 4.2.1. Single Property of the Surrounding Rock

#### 4.2.2. Effect of Rock Quality

## 5. Conclusions

- (1)
- Through the analysis of the stress and strain monitoring results of the YK315 + 710 section of the HTG tunnel, the stress values of certain monitoring points were small, while the strain ratio was large, according to the calculation method of the original UC. The calculated bias factor is meaningless.
- (2)
- After analyzing the root cause of the bias tunnel hazard, we proposed a new practical bias factor. This bias factor clearly indicates the degree of asymmetry of the maximum pressure on both sides of the tunnel design.
- (3)
- Numerical simulation calculations were performed on the target section, and the numerical simulation results and the variable coefficients calculated from the field monitoring data were compared and verified. We found that the variable coefficients were very close.
- (4)
- The influences of the terrain factors (slope angle and cover thickness) and rock properties (single rock property and rock quality) on the UC were studied using numerical simulations. The results indicate that the slope angle, overburden thickness, and elastic modulus significantly affected the bias degree, while other factors had little effect.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 11.**Stress and strain distributing graph. (

**a**) Stress between the surrounding rock and primary support. (

**b**) Stress between the primary support and second lining. (

**c**) Strain of the second lining.

**Figure 14.**Variation curve of the UC when the physical and mechanical parameters change under the condition of V-level surrounding rock. (

**a**) Modulus of elasticity. (

**b**) Poisson′s ratio. (

**c**) Cohesion. (

**d**) Internal friction angle. (

**e**) Bulk density.

Monitoring Points in the Deep-Buried Side | Pressure/kPa | Monitoring Points in the Shallow-Buried | Pressure/kPa | Stress Ratio |
---|---|---|---|---|

RP-3 | (missed) | RP-2 | 36.2 | - |

RP-5 | 13.2 | RP-4 | 9 | 1.47 |

RP-7 | 31.2 | RP-6 | 33.1 | 1.06 |

RP-9 | 14.7 | RP-8 | 29.7 | 2.02 |

Monitoring Points in the Deep-Buried Side | Pressure/kPa | Monitoring Points in the Shallow-Buried Side | Pressure/kPa | Stress Ratio |
---|---|---|---|---|

PS-2 | 67.3 | PS-3 | 37.2 | 1.81 |

PS-4 | 50.7 | PS-5 | 27.9 | 1.82 |

PS-6 | 88.1 | PS-7 | 17.5 | 5.03 |

PS-8 | 151.9 | PS-9 | 138.4 | 1.10 |

PS-10 | 79.9 | PS-11 | 66.1 | 1.21 |

Monitoring Points in the Deep-Buried Side | Strain/με | Monitoring Points in the Shallow-Buried Side | Strain/με | Strain Ratio |
---|---|---|---|---|

SLS-2 | 59 | SLS-6 | 41 | 1.44 |

SLS-3 | 70 | SLS-7 | 24 | 2.92 |

SLS-4 | 50 | SLS-8 | 32 | 1.56 |

SLS-5 | 36 | SLS-9 | 41 | 1.14 |

Material | Bulk Density/kN∙m^{−3} | Elasticity Modulus/Gpa | Poisson’s Ratio | Internal Friction Angle/kPa | Internal Friction/° |
---|---|---|---|---|---|

Surrounding rock | 19 | 1 | 0.4 | 100 | 23 |

Primary support | 22 | 24 | 0.2 | ||

Second lining | 25 | 31 | 0.2 |

Interface | Normal Stiffness Modulus/kN∙m^{−3} | Shear Stiffness Modulus/kN∙m^{−3} |
---|---|---|

Interface between the surrounding rock and primary support | 100,000 | 30,000 |

Interface between the primary support and second lining | 300,000 | 12,500 |

Type of Stress or Strain | Pressure between the Surrounding Rock and Primary Support/kPa | Pressure between the Primary Support and Second Lining/kPa | Strain of the Second Lining/με |
---|---|---|---|

N_{d} | 36.2 | 138.4 | 70 |

N_{s} | 31.2 | 151.9 | 41 |

Unsymmetrical coefficient | 1.16 | 1.10 | 1.71 |

Type of Stress or Strain | Pressure between the Surrounding Rock and Primary Support/kPa | Pressure between the Primary Support and Second Lining/kPa | Strain of the Second Lining/με |
---|---|---|---|

N_{d} | 91.4 | 195.29 | 89.1 |

N_{s} | 81.5 | 211.85 | 65.4 |

Unsymmetrical coefficient | 1.12 | 1.09 | 1.36 |

Rock Grade | Bulk Density/kN∙m^{−3} | Deformation Modulus/Gpa | Poisson’s Ratio | Internal Friction Angle/kPa | Internal Friction/° |
---|---|---|---|---|---|

V | 17–20 | 1–2 | 0.35–0.45 | 50–200 | 20–27 |

Rock Quality Classification | Bulk Density/kN∙m^{−3} | Deformation Modulus/Gpa | Poisson’s Ratio | Internal Friction Angle/kPa | Internal Friction/° |
---|---|---|---|---|---|

High quality | 20 | 2 | 0.35 | 200 | 27 |

Middle quality | 18.5 | 1.5 | 0.4 | 125 | 23.5 |

Low quality | 17 | 1 | 0.45 | 50 | 20 |

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**MDPI and ACS Style**

Zhang, T.; Nie, L.; Zhang, M.; Dai, S.; Xu, Y.; Du, C.; Rui, X.; He, Y.
The Unsymmetrical Coefficient of Unsymmetrical-Loaded Tunnel Based on Field Monitoring and Numerical Simulation. *Symmetry* **2020**, *12*, 1793.
https://doi.org/10.3390/sym12111793

**AMA Style**

Zhang T, Nie L, Zhang M, Dai S, Xu Y, Du C, Rui X, He Y.
The Unsymmetrical Coefficient of Unsymmetrical-Loaded Tunnel Based on Field Monitoring and Numerical Simulation. *Symmetry*. 2020; 12(11):1793.
https://doi.org/10.3390/sym12111793

**Chicago/Turabian Style**

Zhang, Tao, Lei Nie, Min Zhang, Shulin Dai, Yan Xu, Chao Du, Xiangjian Rui, and Yuanyuan He.
2020. "The Unsymmetrical Coefficient of Unsymmetrical-Loaded Tunnel Based on Field Monitoring and Numerical Simulation" *Symmetry* 12, no. 11: 1793.
https://doi.org/10.3390/sym12111793