# Failure Mechanism Analysis and Optimization Analysis of Tunnel Joint Waterstop Considering Bonding and Extrusion

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## Abstract

**:**

## 1. Introduction

## 2. Analysis of the Working Mechanism of the Buried Waterstop

#### 2.1. The Working State of the Buried Waterstop

#### 2.2. Waterproof Mechanism of a Buried Waterstop

- (1)
- Extrusion sealing: in a similar way to the sealing principle of the shield tunnel rubber gasket [28,29], the rubber sealing belt transfers pressure to its contact surface. When extrusion occurs between the waterstop and the concrete lining, contact pressure is generated. Without considering the bonding force between the waterstop belt and concrete, leakage occurs when the water pressure is greater than the contact pressure (Figure 2a).
- (2)
- Bonding water plugging: There is a bond between the contact surface of the buried waterstop and the concrete lining. Without considering the sealing of the waterstop belt, when the water pressure is greater than the bond force, the bond area experiences “intact–damage–failure” and then leakage occurs (Figure 2b).

**Figure 2.**Waterproofing mechanism of a waterstop. (

**a**) Extrusion sealing, (

**b**) Bonding water plugging.

_{wl}≥ γP

_{w}

_{wl}= F + C

_{wl}is the water infiltration resistance, P

_{w}is the theoretical water pressure, γ is the safety factor, F is the contact pressure, and C is the adhesion force. At the same time, the long seepage path formed by the complex cross-sectional form of the waterstop can improve the waterproof reliability of the joint, remove the head pressure, and increase the difficulty for groundwater to seep through the tunnel joint.

## 3. Analysis of Failure Characteristics of a Buried Waterstop

#### 3.1. Bonding Strength Test and Initial Contact Pressure Calculation

#### 3.1.1. Adhesive Strength Test of Rubber and Concrete

#### 3.1.2. Initial Contact Pressure

#### 3.2. Finite Element Analysis of Force and Deformation of Waterstop

#### 3.2.1. Finite Element Model

_{c}is 30 GPa, and Poisson’s ratio ν

_{c}is 0.2. Lining failure is simulated in ABAQUS using the concrete damage plastic model [31]. Among the damage plasticity parameters, the eccentricity e

_{f}, the ratio of biaxial to uniaxial compressive strength f

_{b0}/f

_{c0}, and the coefficient k use default values of 0.1, 1.16, and 0.667, respectively; and the viscosity parameter μ

_{c}is set to 0.005 based on ABAQUS implicit solution; the expansion angle ψ is set to 30°; and the stress–strain curves of concrete uniaxial compression and tension are selected for the concrete design code [32], as shown in Table 2, where σ

_{c}and σ

_{t}are compressive stress and tensile stress and ${\mathrm{\epsilon}}_{\mathrm{c}}^{\mathrm{in}}$, and ${\mathrm{\epsilon}}_{\mathrm{t}}^{\mathrm{in}}$ are inelastic strain and cracking strain, respectively.

_{10}(l

_{1}− 3) + C

_{01}(l

_{2}− 3)

_{1}and l

_{2}are invariants of the strain tensor, and C

_{10}and C

_{01}are mechanical properties constants of materials. The relationship between elastic modulus E

_{0}and material constant can be obtained from the incompressibility of rubber:

_{0}= 6(C

_{10}+ C

_{01})

_{0}can be determined by rubber hardness H

_{A}, and its relationship is as follows:

_{0}= (15.75 + 2.15H

_{A})/(100 − H

_{A})

_{10}/C

_{01}generally takes 0.25 for better fitting [33]. It can be calculated that C

_{10}= 0.484 MPa and C

_{01}= 0.121 MPa.

^{6}MPa, the tangential stiffness is 4.33 × 10

^{6}MPa, the normal bonding force is 0.095 MPa, the tangential bonding force is 0.211 MPa, and the plastic displacement is 0.001 mm. Self-contact is set in the middle hole of the waterstop, and the friction coefficient is 0.8.

#### 3.2.2. Damage Failure Analysis of Concrete Lining

#### 3.2.3. Deformation Stress Characteristics of the Waterstop

#### 3.2.4. Deformation Stress on the Waterstop

#### 3.3. Waterproof Capacity Analysis of the Waterstop

#### 3.3.1. Long-Term Resistance of the Waterstop to Seepage

#### 3.3.2. Short-Term Resistance of the Waterstop to Seepage

_{c}is the deformation when the short-term seepage resistance is equal to the long-term seepage resistance, Mises

_{max}is the maximum von Mises stress on the waterstop, the allowable deformation t

_{a}is the maximum deformation when the hose can meet the service life requirements, and ${\mathrm{P}}_{\mathrm{wl}}^{\mathrm{lt}}$

_{max}is the maximum short-term seepage resistance within the allowable deformation.

- (1)
- The stress on waterstop I at the maximum tensile and compressive deformation does not reach the dangerous level. After the settlement deformation reaches 29 mm, the stress exceeds the dangerous level, which may make it difficult for the tunnel joint to meet the service life requirements.
- (2)
- When the deformation of the tunnel joint is greater than the critical deformation, the short-term resistance to water seepage is greater than the long-term resistance to water seepage. Therefore, if the waterstop can maintain a certain amount of deformation for a long time, it may be more conducive to the waterproofing of the tunnel joint.
- (3)
- Except for the long-term water seepage resistance, the difference between working conditions 1 and 2 is small, which means that the initial contact pressure has little effect on the waterproofing ability of the waterstop after deformation.

## 4. Optimization Analysis of the Waterproof Performance of the Waterstop

#### 4.1. Dimensional Optimization of the Waterstop

#### 4.2. Optimal Analysis of the Adhesion between the Waterstop and Concrete

## 5. Conclusions

- (1)
- The waterproofing ability of the buried waterstop mainly depends on its resistance to seepage, and the resistance involves contact pressure and bonding force between the waterstop and concrete. According to whether the tunnel joint is deformed or not, it can be classified as short-term or long-term seepage resistance.
- (2)
- The deformation force of the waterstop is mainly concentrated between the first ribs on the left and right sides. The deformation does not completely destroy the bond between the waterstop belt and concrete, but only reduces the waterproofing reliability of the waterstop. Therefore, the waterproofing ability of the waterstop depends on its long-term resistance to water seepage.
- (3)
- The stress on the waterstop may exceed the dangerous level when the deformation is large, making it difficult for the tunnel joints to meet the service life requirements. For example, the stress on the waterstop I in this paper will exceed the dangerous level after the settlement deformation reaches 29 mm.
- (4)
- The long-term resistance of the waterstop to water seepage is the smallest at the vault, first increases continuously along with the lining profile and then remains unchanged. When the deformation of the tunnel joint is greater than the critical deformation, the short-term resistance to water seepage is greater than the long-term resistance to it.
- (5)
- Reducing the thickness of the waterstop and increasing the size of the hole in the waterstop are beneficial to improving the deformation and stress state of the waterstop and to reducing the damage to the bond between the waterstop and the concrete. Increasing the adhesion between the waterstop and the concrete can significantly improve the long-term resistance of the waterstop to water seepage, but at the same time, the deformation stress on the waterstop will increase.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of the waterproof structure of the mountain tunnel joints. (

**a**) Deformation joint, (

**b**) Construction joint.

**Figure 4.**The deformation contact pressure of the waterstop. (

**a**) Tensile contact pressure. (

**b**) Compressive contact pressure. (

**c**) Settling contact pressure.

**Figure 10.**Damage cloud diagram of concrete stiffness in working condition 1. (

**a**) 1-1 concrete compression damage. (

**b**) 1-1 concrete tensile damage. (

**c**) 1-2 concrete compression damage. (

**d**) 1-2 concrete tensile damage. (

**e**) 1-3 concrete compression damage. (

**f**) 1-3 concrete tensile damage.

**Figure 11.**Condition 1 von Mises stress cloud diagram (unit: MPa). (

**a**) 1-1 stress cloud diagram. (

**b**) 1-2 stress cloud diagram. (

**c**) 1-3 stress cloud diagram.

**Figure 12.**Damage cloud diagram of bonding stiffness in working condition 1. (

**a**) 1-1 bonding stiffness damage. (

**b**) 1-2 bonding stiffness damage. (

**c**) 1-3 bonding stiffness damage.

**Figure 23.**Compression deformation stress on the waterstop under different bonding force conditions.

Conditions | 1 | 2 | 3 | Bonding Strength/MPa |
---|---|---|---|---|

Tensile specimen | 0.091 | 0.101 | 0.097 | 0.096 |

Shear specimen | 0.215 | 0.208 | 0.211 | 0.211 |

σ_{c} | ${\mathsf{\epsilon}}_{\mathbf{c}}^{\mathbf{i}\mathbf{n}}$ | σ_{t} | ${\mathsf{\epsilon}}_{\mathbf{t}}^{\mathbf{i}\mathbf{n}}$ |
---|---|---|---|

14.070 | 0 | 2.030 | 0 |

20.100 | 0.000802 | 2.010 | 0.000028 |

14.637 | 0.002456 | 1.232 | 0.000149 |

10.073 | 0.004080 | 0.849 | 0.000257 |

7.501 | 0.005638 | 0.661 | 0.000359 |

5.931 | 0.007162 | 0.548 | 0.000458 |

4.890 | 0.008668 | 0.473 | 0.000556 |

4.153 | 0.010165 | 0.419 | 0.000653 |

3.607 | 0.011655 | 0.378 | 0.000749 |

3.186 | 0.013141 | 0.346 | 0.000846 |

Working Conditions | Initial Contact Pressure (MPa) | Deformation Types | Deformation (mm) |
---|---|---|---|

1-1 | Tensile | 20 | |

1-2 | 0.005 | Compression | 10 |

1-3 | Settlement | 30 | |

2-1 | Tensile | 20 | |

2-2 | 0.048 | Compression | 10 |

2-3 | Settlement | 30 |

Conditions | ${\mathbf{P}}_{\mathbf{w}\mathbf{l}}^{\mathbf{s}\mathbf{t}}$ (MPa) | t_{c} (mm) | Mises_{max} (MPa) | t_{a} (mm) | ${\mathbf{P}}_{\mathbf{w}\mathbf{l}}^{\mathbf{l}\mathbf{t}}$_{max} (MPa) |
---|---|---|---|---|---|

1-1 | 2.7 | 1.78 | 20.0 | 1.48 | |

1-2 | 0.101 | 4.7 | 1.82 | 10.0 | 0.53 |

1-3 | 2.0 | 2.05 | 29.5 | 6.92 | |

2-1 | 3.1 | 1.75 | 20.0 | 1.45 | |

2-2 | 0.144 | 4.7 | 1.89 | 10.0 | 0.51 |

2-3 | 1.4 | 2.00 | 29.9 | 6.61 |

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**MDPI and ACS Style**

Wu, Y.; Wu, H.; Chu, D.; Feng, S.; Zhang, J.; Wu, H.
Failure Mechanism Analysis and Optimization Analysis of Tunnel Joint Waterstop Considering Bonding and Extrusion. *Appl. Sci.* **2022**, *12*, 5737.
https://doi.org/10.3390/app12115737

**AMA Style**

Wu Y, Wu H, Chu D, Feng S, Zhang J, Wu H.
Failure Mechanism Analysis and Optimization Analysis of Tunnel Joint Waterstop Considering Bonding and Extrusion. *Applied Sciences*. 2022; 12(11):5737.
https://doi.org/10.3390/app12115737

**Chicago/Turabian Style**

Wu, Yimin, Haiping Wu, Dinghai Chu, Sheng Feng, Junjian Zhang, and Haoran Wu.
2022. "Failure Mechanism Analysis and Optimization Analysis of Tunnel Joint Waterstop Considering Bonding and Extrusion" *Applied Sciences* 12, no. 11: 5737.
https://doi.org/10.3390/app12115737