# Effect of Voids Behind Lining on the Failure Behavior of Symmetrical Double-Arch Tunnels

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Study

#### 2.1. Experimental Schemes

#### 2.2. Experimental Process

_{l}in the model tests was selected as 40. A type of acceptable modeling material was developed for satisfying the law of similarity; that is, a mixture of barite powder, silica sand, and petroleum jelly in a weight ratio of 4:10:1, and a mixture of water and gypsum in a weight ratio of 0.9:1 was selected for the lining. Various laboratory tests were performed, including static triaxial tests to determine the elastic modulus and Poisson’s ratio, direct shear tests to determine the cohesion and friction angle, and density tests to determine the unit weight of the ground. A set of compressive strength tests on cylinders with different weight ratios were carried out to achieve the elastic modulus and uniaxial strength of the lining. The model parameters of the lining and the surrounding soils are summarized in Table 1. Note that it is difficult to completely meet the similarity criteria. The unit weight of the model lining is 8.3 KN/m

^{3}, which is not strictly consistent with the prototype. However, the influence of the unit weight of the lining on the failure behavior of the lining was generally negligible.

#### 2.3. Experimental Results

#### 2.3.1. Earth Pressure Distribution

#### 2.3.2. Distribution of Bending Moments

#### 2.3.3. Lining Failure and Cracking

## 3. Numerical Study

#### 3.1. Numerical Model

#### 3.2. Numerical Schemes

#### 3.3. Numerical Results

#### 3.3.1. Effect of Void Location

#### 3.3.2. Effect of Void Size

## 4. Comparisons with Asymmetrical Double-Arch Tunnels

#### 4.1. Without Voids behind the Lining

#### 4.2. Without a Void on the Top of the Central Wall

## 5. Summary and Conclusions

- (1)
- The existence of a void behind the central wall, affecting the re-distribution of the earth pressure compared with the case without voids, results in the concentration of stress on both sides of the void located on the top of the central wall, associated with it the emergence of cracks in the lining on the upper right and left corners of the central wall of symmetrical double-arch tunnels.
- (2)
- Due to the presence of voids behind the lining, significant changes in the internal forces in the lining were found at the areas in close vicinity of the void, whereas only a few changes were found at the invert and central wall. The lining at the bottom of the central wall of the symmetrical double-arch tunnel, which is regarded as the weak part, suffered the most severe damage.
- (3)
- Given that the presence of a void can generally preclude any symmetry, the cracks adjacent to the central wall of symmetrical double-arch tunnels are more sensitive to the location of the void. With the growth in the angle of voids, the positive bending moments in the lining on the inside of the void increased, and the cracks are likely to appear at the outer fiber of the lining.
- (4)
- Compared with asymmetrical double-arch tunnels, the introduction of a void behind the central wall leads to lighter damage and later emergence of cracks in the lining on the upper left corner of the central wall. The location of the initial cracking of the double-arch tunnels is basically the same, while the lining failure of the large-section tunnel seems to be more complicated.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Displacement testing devices: (

**a**) Six displacement meters fixed on a metal plate; (

**b**) two testing devices installed inside the tunnel; and (

**c**) connection with the strain indicator and computer.

**Figure 5.**The layout of measuring points (MPs) and the model of the lining (unit: m): (

**a**) Location of strain gauges, pressure cells, and displacement meters; and (

**b**) model entity of the symmetrical double-arch tunnel.

**Figure 11.**Failure patterns of the symmetrical double-arch tunnel lining with voids at different locations: (

**a**) NT 1, (

**b**) NT 2, (

**c**) NT 3, (

**d**) NT 4, (

**e**) NT 5, and (

**f**) NT 6 (NT—Numerical Test).

**Figure 12.**Distribution of minimum principal strain with different void locations (Numerical Tests 2–5): (

**a**) NT 2; (

**b**) NT 3; (

**c**) NT 4; and (

**d**) NT 5.

**Figure 13.**Failure patterns of the symmetrical double-arch tunnel lining with different void size at the vault: (

**a**) 15°; (

**b**) 25°; (

**c**) 30°; and (

**d**) 35°.

**Figure 15.**Distribution of lining internal force in the initial state: (

**a**) NT 1; (

**b**) NT 2; (

**c**) NT 3; (

**d**) NT 4; (

**e**) NT 5; and (

**f**) NT 6.

**Figure 16.**Cross-section of the asymmetrical double-arch tunnel and model entity of the lining (unit: m): (

**a**) Cross-section of the prototype and (

**b**) asymmetrical double-arch tunnel lining in the model.

**Figure 17.**The failure pattern of the double-arch tunnels without voids behind the lining: (

**a**) Symmetrical double-arch tunnel and (

**b**) asymmetrical double-arch tunnel.

**Figure 18.**The failure pattern of the double-arch tunnels with a void on the top of the central wall: (

**a**) Symmetrical double-arch tunnel and (

**b**) asymmetrical double-arch tunnel.

Materials | Unit Weight (kN/m^{3}) | Elastic Modulus (GPa) | Poisson’s Ratio | Cohesion (kPa) | Friction Angle (°) |
---|---|---|---|---|---|

Soil | 18 | 0.0068 | 0.37 | 4.6 | 24 |

Lining | 8.3 | 0.8350 | 0.20 | — | — |

Materials | Unit Weight (kN/m^{3}) | Elastic Modulus (GPa) | Poisson’s Ratio | Cohesion (kPa) | Friction Angle (°) |
---|---|---|---|---|---|

Soil | 18 | 0.27 | 0.37 | 182 | 24 |

Lining | 25 | 33.5 | 0.20 | — | — |

Scheme | Void Location | Void Size θ (°) |
---|---|---|

Numerical Test 1 | None (base case) | — |

Numerical Test 2 | Central wall (void 1) | — |

Numerical Test 3 | Right haunch (void 2) | 20 |

Numerical Test 4 | Right shoulder (void 3) | 20 |

Numerical Test 5 | Vault (void 4) | 20 |

Numerical Test 6 | Left shoulder (void 5) | 20 |

Numerical Tests 7–10 | Vault (void 4) | 15, 25, 30, 35 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, X.; Ye, Z.; Min, B.; Xu, Y.
Effect of Voids Behind Lining on the Failure Behavior of Symmetrical Double-Arch Tunnels. *Symmetry* **2019**, *11*, 1321.
https://doi.org/10.3390/sym11101321

**AMA Style**

Zhang X, Ye Z, Min B, Xu Y.
Effect of Voids Behind Lining on the Failure Behavior of Symmetrical Double-Arch Tunnels. *Symmetry*. 2019; 11(10):1321.
https://doi.org/10.3390/sym11101321

**Chicago/Turabian Style**

Zhang, Xu, Zijian Ye, Bo Min, and Youjun Xu.
2019. "Effect of Voids Behind Lining on the Failure Behavior of Symmetrical Double-Arch Tunnels" *Symmetry* 11, no. 10: 1321.
https://doi.org/10.3390/sym11101321