# Investigation into the Bearing Capacity and Mechanics Behavior of the Diaphragm Connection Form of a Utility Tunnel

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## Abstract

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## 1. Introduction

## 2. Engineering Background and Connection Scheme

#### 2.1. Engineering Background

#### 2.2. Introduction of Connection Scheme

#### 2.2.1. Steel Corbel and Rear Expansion Anchor Bolt

#### 2.2.2. Embedded Part and Steel Corbel

#### 2.2.3. Reinforced Concrete Corbel

## 3. Experimental and Numerical Simulation Design

#### 3.1. Experiment Design

#### 3.1.1. Test Conditions

#### 3.1.2. Experimental Materials

#### 3.2. Numerical Simulation Design

## 4. Analysis of Experimental and Numerical Simulation Results

#### 4.1. Steel Corbel and Six Rear Expansion Anchor Bolts

#### 4.1.1. Analysis of Steel Corbel

#### 4.1.2. Analysis of the Anchor Bolt

#### 4.1.3. Analysis of Concrete Damage

#### 4.2. Steel Corbel and Nine Rear Expansion Anchor Bolts

#### 4.2.1. Analysis of Steel Corbel

#### 4.2.2. Analysis of Anchor Bolt

#### 4.2.3. Analysis of Concrete Damage

#### 4.3. Embedded Parts and Steel Corbel

#### 4.3.1. Analysis of Steel Corbel

#### 4.3.2. Analysis of Anchored Bar

#### 4.3.3. Analysis of Concrete Damage

#### 4.4. Reinforced Concrete Corbel

#### 4.5. Scheme Comparison

#### 4.6. Analysis of the Influence of Anchor Bolt Arrangement Form

## 5. Conclusions

- The critical point in the steel corbel and rear expansion anchor bolt connection scheme lies in the connection region, where we observed bolt shear failure and concrete cracking. The number of bolts significantly influences the load-bearing capacity of the steel corbel. Adhering to the criterion that the steel bar and steel plate remain within their respective yield strengths during the elastic working phase and ensuring that the concrete damage area around the bolt remains unconnected, we achieved a bearing capacity of 180 kN when utilizing six rear expansion anchor bolts. However, when employing nine rear expansion anchor bolts, the load-bearing capacity decreased to 170 kN, resulting in a 5.6% reduction in bearing capacity.
- The arrangement of bolts has a notable impact on the structural load-bearing capacity. The upper-side anchor bolts bear larger forces, while the lower-side anchor bolts handle less load. Arranging the six anchor bolts in a configuration of two rows and three columns enhances the load-bearing capacity. Still, avoiding forming a damaged area due to inappropriate bolt spacing is crucial. This study’s recommended transverse bolt spacing falls within the 66.7 mm to 100 mm range. The third row experiences the most significant vertical deformation among the anchor bolts, while the first row exhibits the greatest axial elongation. Deformation in the anchor bolts is predominantly concentrated within the 5 cm to 6 cm range near the bracket. The anchorage depth should not be less than 6 cm. In the case of this scheme, the anchorage depth can be preferably selected from the range of 11 cm to 15 cm.
- The connection scheme involving embedded parts and a steel corbel exhibits robust load-bearing capacity, capable of withstanding a 220 kN load within the elastic stage. The anchor bar demonstrates strong anchoring ability, and the steel corbel experiences minimal deformation. Anchor bar deformation primarily concentrates within the 5 cm range near the corbel, with the upper-side anchor bar showing the most significant deformation.
- The reinforced concrete corbel connection scheme boasts a bearing capacity of 240 kN, with its load-bearing capacity primarily governed by crack formation. Initially, cracks emerge symmetrically on both sides of the corbel, progressively extending to encompass the width and height of the corbel structure.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Structural diagram of embedded parts. (

**a**) Embedded part schematic; (

**b**) embedded part and steel corbels.

**Figure 11.**Model representation. (

**a**) Steel corbel and 6 rear expansion anchor bolts connection; (

**b**) steel corbel and 9 rear expansion anchor bolts connection; (

**c**) embedded parts and steel corbel connection; (

**d**) reinforced concrete corbel connection.

**Figure 13.**Test of mechanical properties of concrete. (

**a**) Cube compressive strength test; (

**b**) axial compressive strength test-1; (

**c**) axial compressive strength test-2; (

**d**) elastic modulus test.

**Figure 15.**Displacement monitoring scheme. (

**a**) Displacement monitoring points; (

**b**) splaying amount indicates.

**Figure 18.**Failure pattern and stress displacement distribution of anchor bolts. (

**a**) Bolt shear failure; (

**b**) gasket deformation; (

**c**) maximum principal stress; (

**d**) minimum principal stress; (

**e**) vertical displacement; (

**f**) horizontal displacement.

**Figure 21.**Failure pattern of concrete. (

**a**) Cracking of concrete; (

**b**) crushing of concrete; (

**c**) compression damage of concrete (300 kN); (

**d**) tensile damage of concrete (300 kN).

**Figure 26.**Failure pattern and stress displacement distribution of anchor bolts. (

**a**) Bolt shear failure; (

**b**) gasket deformation; (

**c**) maximum principal stress; (

**d**) minimum principal stress; (

**e**) vertical displacement; (

**f**) horizontal displacement.

**Figure 29.**Failure pattern of concrete. (

**a**) Cracking of concrete; (

**b**) crushing of concrete; (

**c**) compression damage of concrete (300 kN); (

**d**) tensile damage of concrete (300 kN).

**Figure 34.**Cracking morphology and deformation. (

**a**) Left contact area; (

**b**) right contact area; (

**c**) deformation of corbel.

**Figure 35.**Stress of anchor bar. (

**a**) Stress curve of anchor bar; (

**b**) stress distribution of anchor bar.

**Figure 36.**Displacement of anchor bar. (

**a**) Displacement curve of anchor bar; (

**b**) vertical displacement of anchor bar.

**Figure 38.**Surface damage of concrete. (

**a**) Compression damage of concrete (350 kN); (

**b**) tensile damage of concrete (350 kN).

**Figure 41.**Tensile damage of concrete. (

**a**) Load 100 kN; (

**b**) load 150 kN; (

**c**) load 220 kN; (

**d**) load 300 kN.

**Figure 47.**Displacement of anchor bolt (m). (

**a**) Mode 1 vertical displacement; (

**b**) mode 1 horizontal displacement; (

**c**) mode 2 vertical displacement; (

**d**) mode 2 horizontal displacement.

**Figure 48.**Surface damage of concrete. (

**a**) Compression damage of concrete in mode 1 (300 kN); (

**b**) tensile damage of concrete in mode 1 (300 kN); (

**c**) compression damage of concrete in mode 2 (300 kN); (

**d**) tensile damage of concrete in mode 2 (300 kN).

**Figure 49.**Internal damage of concrete. (

**a**) Mode 1 load 200 kN; (

**b**) mode 1, load 300 kN; (

**c**) mode 2, load 200 kN; (

**d**) mode 2, load 300 kN.

Specimen Number | Leading Feature | Size of Reinforced Concrete Specimen | Grade of Concrete Segment | Grade of Concrete Corbel |
---|---|---|---|---|

1 | Steel corbel and 6 rear expansion anchor bolts | 1.5 m × 1.2 m × 0.3 m | C50 | |

2 | Steel corbel and 9 rear reamed anchor bolts | C50 | ||

3 | Embedded part and steel corbel | C50 | ||

4 | Reinforced concrete corbel | C50 | C50 |

Material | Elastic Modulus (GPa) | Poisson’s Ratio | Yield Strength (MPa) | Tensile Strength (MPa) | Plastic Strain |
---|---|---|---|---|---|

Q355B steel plate | 206 | 0.25 | 380 | 503 | 0.1 |

Grade 8.8 bolt | 200 | 0.25 | 640 | 800 | 0.12 |

HRB400 | 200 | 0.3 | 400 | 540 | 0.075 |

HPB300 | 210 | 0.3 | 300 | 420 | 0.1 |

Connection Schemes | Mechanical Property | Construction Convenience | Conclusion |
---|---|---|---|

Steel corbel and six rear expansion anchor bolts | Following elastic design principles, the bearing capacity of this configuration is determined to be 180 kN. The ultimate failure mode involves significant shear deformation of the bolt, tearing of the anchor bolt sleeve, and cracking of the concrete surface. | The anchor bolt requires fewer drilled holes, making it easier to install. | Its use is recommended, and there is potential for further optimization. |

Steel corbel and nine rear expansion anchor bolts | The bearing capacity is 170 kN, and the failure is characterized by severe shear deformation of bolts, deformation of the bolt sleeve, cracking, and the propagation of cracks on the concrete surface. | The anchor bolt requires more drilling holes, which leads to increased installation difficulty and higher costs. | The bearing capacity is reduced, the cost is high, and its use is not recommended. |

Embedded part and steel corbel | The bearing capacity is up to 220 kN, and the corbel exhibits minimal deformation and excellent mechanical properties. | On-site welding quality is challenging to ensure, and the construction process is inconvenient. | After addressing the construction convenience issue, it is not recommended as a whole based on the specific circumstances. |

Reinforced concrete corbel | Load capacity 240 kN | It needs to be prefabricated simultaneously with the segment, which can be inconvenient for transportation and installation. | It is necessary to address the issue of construction convenience; as a whole, it is not recommended. |

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**MDPI and ACS Style**

Dai, Y.; Zeng, Y.; Shi, B.; Li, H.
Investigation into the Bearing Capacity and Mechanics Behavior of the Diaphragm Connection Form of a Utility Tunnel. *Buildings* **2024**, *14*, 695.
https://doi.org/10.3390/buildings14030695

**AMA Style**

Dai Y, Zeng Y, Shi B, Li H.
Investigation into the Bearing Capacity and Mechanics Behavior of the Diaphragm Connection Form of a Utility Tunnel. *Buildings*. 2024; 14(3):695.
https://doi.org/10.3390/buildings14030695

**Chicago/Turabian Style**

Dai, Yongxing, Yi Zeng, Bolun Shi, and Hongbo Li.
2024. "Investigation into the Bearing Capacity and Mechanics Behavior of the Diaphragm Connection Form of a Utility Tunnel" *Buildings* 14, no. 3: 695.
https://doi.org/10.3390/buildings14030695