# Deformation Characteristics Analysis of Temporary Support in Unsymmetrical Loading Tunnel Excavation under Composite Support

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Engineering Background and Excavation Method

#### 2.1. Engineering Geology

#### 2.2. Excavation Method of Shallow-Buried Large-Section Tunnel

^{2}. Due to the coupling effect of rock mass fragmentation and lateral pressure of unilateral hillside, the surrounding rock self-stability of this large cross-section tunnel is poor, and the supporting structure is at risk of migration. During the construction, the pipe roof pre-grouting is gradually used to reinforce the surrounding rock with the advancement of the tunnel face. The excavation process of the two-step CDM is shown in Figure 5.

^{4}. The steel grid is made of Φ25 mm main reinforcement and Φ14 mm connecting reinforcement. Its elastic modulus is 210 GPa and the cross-section moment of inertia is 3686.76 cm

^{4}.

## 3. Mechanical Analysis of Supporting Structure

#### 3.1. Pipe Roof

E_{g} | is the equivalent elastic modulus of the grouting steel pipe, |

γ_{g} | is the equivalent weight of the grouting steel pipe, |

E_{1} | is the elastic modulus of the steel pipe, E_{1} = 210 GPa, |

I_{1} | is the moment of inertia of the steel pipe section, I_{1} = 1.77 × 10^{−6} m^{4}, |

γ_{1} | is the weight of the steel pipe, γ_{1} = 78.5 kN/m^{3}, |

A_{1} | is the cross-sectional area of the steel pipe, A_{1} =1.31 × 10^{−3} m^{2}, |

E_{2} | is the elastic modulus of the cement mortar, E_{2} = 2.8 × 10^{4} MPa, |

I_{2} | is the moment of inertia of the filling cement mortar section, I_{2} = 4.91 × 10^{−6} m^{4}, |

γ_{2} | is the weight of the cement mortar, γ_{2} = 20.0 kN/m^{3}, |

A_{2} | is the cross-sectional area of the filling cement mortar, A_{2} = 7.85 × 10^{−3} m^{2}. |

E | is the elastic modulus of the grouting reinforcement area, |

E_{0} | is the elastic modulus of the stratum, E_{0} = 59.4 MPa, |

S_{g} | is the cross-sectional area of the grouting steel pipe, S_{g} = A_{1} + A_{2} = 9.16 × 10^{−3} m^{2}, |

S_{c} | is the cross-sectional area of the support section, S_{c} = l × 2r = 0.4 m^{2}. |

#### 3.2. Steel Grid Support

P | is the structural support resistance, |

K | is the supporting stiffness of the structure, |

u | is the radial displacement of the structure. |

E | is the equivalent elastic modulus of the steel grid, |

t | is the structural thickness of the steel grid, |

v | is the Poisson’s ratio of the steel grid, |

R | is the equivalent radius of the tunnel. |

_{max}of the steel grid can be obtained from Equation (6). Through the equivalence principle, the section form of the steel grid is equivalent to a rectangular section as shown in Figure 12. The yield strength and elastic modulus of the equivalent section form are calculated according to Equations (7) and (8), respectively.

σ_{c} | is the equivalent yield stress of the steel grid, |

σ_{s} | is the yield strength of the steel grid, |

E_{s} | is the elastic modulus of the steel grid, |

A_{s} | is the cross-sectional area of the steel grid, |

A | is the equivalent rectangular cross-sectional area, |

I_{s} | is the moment of inertia of the section, |

I | is the moment of inertia of the equivalent rectangular section. |

#### 3.3. Temporary Steel Support

## 4. Numerical Analysis

#### 4.1. Model Building

#### 4.2. Fundamental Assumption

- (1)
- Each geological layer, pipe roof grouting and solid are regarded as homogeneous and isotropic media.
- (2)
- The deformation and failure of the tunnel surrounding rock, temporary steel support, and pipe roof grouting conform to the classical elastic–plastic theory.
- (3)
- Without considering the influence of disturbance caused by tunnel excavation on the structure itself and the effect of tectonic stress, only considering the influence of self-weight on the structure itself. The initial horizontal stress is calculated by using the surrounding rock gravity in MIDAS software, which can be expressed by Equation (9).

σ_{h} | is the horizontal stress, |

σ_{v} | is the vertical stress, |

μ | is Poisson’s ratio. |

#### 4.3. Constitutive Relation

σ_{1} | is the first principal stress of the material, |

σ_{2} | is the second principal stress of the material, |

σ_{3} | is the third principal stress of the material, |

σ_{s} | is the yield point of the material, and σ_{s} = 235 MPa, |

K | is the shear yield strength of the material. |

τ | is the shear stress on the shear plane, Pa, |

σ | is the normal stress on the shear plane, |

φ | is the internal friction angle, |

σ_{1} | is the first principal stress, |

σ_{3} | is the third principal stress. |

#### 4.4. Calculated Parameters

#### 4.5. Analysis Process

#### 4.5.1. Surrounding Rock Stress

#### 4.5.2. Displacement of Surrounding Rock

#### 4.5.3. Analysis of Mechanical Characteristics in Temporary Steel Support

_{1}, S

_{2,}and S

_{3}) to analyze the principal stress of the temporary steel support. The measuring points S

_{1}and S

_{2}are located at the midpoint of the temporary steel support of the upper and lower bench, respectively. The measuring point S

_{3}is located at the connection of the upper and lower bench. Through the MIDAS’ extraction function, the principal stress results of the temporary steel support are extracted. Figure 25 shows its principal stress change curve in cross-section y = 30 m.

_{3}continued to increase, with a maximum value of −202.7 MPa, which did not reach the yield strength of the I-steel of 235 MPa in terms of value, so the structure is safe. To ensure the construction safety, attention should be paid to the reinforcement of the temporary steel support at the joint of the upper and lower bench, and the transverse steel support can be set up at the joint if necessary.

## 5. Field Monitoring

#### 5.1. Measurement Method

_{1}and D

_{2}) are set to measure the spandrel settlement. The positions of the monitoring points in the field are consistent with those in the process of numerical simulation.

#### 5.2. Analysis of Monitoring Results

#### 5.2.1. Horizontal Convergence

#### 5.2.2. Spandrel Settlement

_{1}changed from settlement to uplift gradually, which indicated that the surrounding rock on the left spandrel was uplifted. Before the end of the excavation, the uplift value became stable gradually. (2) Affected by the slope bias, when excavating the right upper bench ③, the settlement of the right spandrel (measurement point D

_{2}) increased rapidly. When excavating the right lower bench ④, the settlement value of monitoring point D

_{2}continued to increase, while the growth rate slowed down and stabilized before all the excavation was completed. (3) The settlement value obtained by numerical simulation was smaller than the measured value, while the variation law was the same. Considering that the geological strata in the actual tunnel are more complex than that in the numerical simulation, the difference in settlement value is acceptable, which verifies the correctness of the numerical simulation calculation.

## 6. Conclusions

- (1)
- In the process of simulating tunnel excavation with or without temporary steel support, the stress distribution of the surrounding is basically the same. The existence of steel supports changes the maximum tensile stress of the left spandrel from 0.35 MPa to 0.16 MPa, a decrease of 54.3%. At the same time, the area of the tensile stress area is reduced, which is more conducive to the stability of the surrounding rock.
- (2)
- Affected by the slope bias and the excavation sequence, the maximum settlement of the surrounding rock is distributed on the right spandrel. The existence of temporary steel support makes the maximum settlement of surrounding rock change from −31.23 mm to −7.4 mm, and the bottom uplift change from 88.58 mm to 66.18 mm, which are reduced by 76.3% and 25.3%, respectively.
- (3)
- During the excavation process of the tunnel using the two-step CDM, the change law of the principal stress at the middle point of the temporary steel support of the upper and lower bench is basically the same, showing a “bench-type” phenomenon. Due to the phenomenon of stress concentration, the principal stress value at the joint of the temporary steel support of the upper and lower bench is the largest. Ji Xinbo et al. [39,40] have performed similar research and put forward some measures to enhance the stability of temporary steel supports, such as adding lateral supports or increasing the size of I-steels.
- (4)
- Tunnel excavation methods and excavation sequences have different effects on the deformation of temporary steel supports. When the excavation method (two-step CDM) is used in this paper, the deformation of the steel support on the upper bench undergoes four stages: convergence, expansion, convergence, and stabilization; and the deformation of the steel support on the lower bench undergoes five stages: convergence, expansion, convergence, expansion, and stabilization. However, when the tunnel is excavated by blasting [31,41], the failure process of the temporary steel support goes through four stages of development. Additionally, when adopting CRD excavation method [23], the deformation process is different. This paper enriches the deformation characteristics of temporary steel supports under different excavation methods.
- (5)
- There are some errors between the field monitoring data and the numerical simulation, but the variation law is basically the same, which verifies the rationality of the numerical simulation. The research results can provide guidance for similar engineering support.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 10.**The structure and layout of the steel grid. Notes: a—Φ25 mm main reinforcement, b—Φ14 mm connect reinforcement, and c—Φ22 mm connecting reinforcement.

**Figure 11.**Mechanical calculation diagram of steel grid. Notes: X

_{1}—shearing force, X

_{2}—axial force, X

_{3}—bending moment.

**Figure 14.**Mechanical calculation diagram of I-steel. Notes: X

_{1}—shearing force, X

_{2}—axial force, X

_{3}—bending moment.

**Figure 17.**Schematic diagram of tunnel excavation and support. Notes: a—steel grid; b—temporary steel support; c—tunnel side wall; d—feet-lock bolt; e—anchors; f—fixed support; g—grouting area; h—No.18 I-steel; i—connect reinforcement.

Strata | Thickness/m | Representative Symbols |
---|---|---|

Subgrade filling | 0.7 | Q_{1} |

Completely weathered mudstone | 1.7 | Q_{2} |

Intensely weathered mudstone | 7.9 | Q_{3} |

Moderately weathered calcareous mudstone | 67.4 | Q_{4} |

Gravel-containing silty clay | 3.0 | Q_{5} |

Materials | Diameter/mm | Elastic Modulus/GPa | Yield Strength/MPa |
---|---|---|---|

Anchors | 22 | 210 | 235 |

Component | Size |
---|---|

Diameter of a single steel pipe | D = 108 mm |

The thickness of a single steel pipe | δ = 4 mm |

Length of a single steel pipe | L = 40 m |

Circumferential spacing of a single steel pipe | L = 0.4 m |

Material | E/MPa | µ | γ/kN·m^{−3} | c/kPa | φ/(°) |
---|---|---|---|---|---|

Grouting steel pipe | 76225 | 0.20 | 28.4 | ||

Reinforcement area | 1805 | 0.30 | 21.0 | 200 | 28 |

Type | Section Area/cm^{2} | Cross-Section Moment of Inertia/cm^{4} | Elastic Modulus/GPa | Yield Strength/MPa |
---|---|---|---|---|

Φ25 mm main reinforcement | 19.63 | 2954.45 | 210 | 400 |

Φ14 mm connect reinforcement | 12.32 | 732.31 | 210 | 400 |

Type | Section Area/cm^{2} | Cross-Section Moment of Inertia /cm^{4} | Elastic Modulus/GPa | Yield Strength /MPa |
---|---|---|---|---|

No. 18 I-steel | 30.43 | 1659.45 | 210 | 235 |

Specimen | Diameter/mm | Failure Load/kN | Peak Stress/MPa | Poisson Ratio µ | Elastic Modulus/MPa |
---|---|---|---|---|---|

1 | 54.7 | 99.734 | 42.4 | 0.188 | 54.527 |

2 | 54.7 | 107.324 | 45.7 | 0.315 | 69.333 |

3 | 54.7 | 94.974 | 40.4 | 0.188 | 54.305 |

Material | E/MPa | µ | γ/kN·m^{−3} | c/kPa | φ/ (°) |
---|---|---|---|---|---|

Subgrade filling | 1.8 | 0.15 | 16.9 | 17 | 10 |

Completely weathered mudstone | 4.5 | 0.30 | 20.5 | 28 | 16 |

Intensely weathered mudstone | 9.1 | 0.20 | 20.4 | 28 | 27 |

Moderately weathered calcareous mudstone | 59.4 | 0.23 | 24.0 | 150 | 33 |

Gravel-containing silty clay | 20.0 | 0.25 | 19.0 | 39 | 20 |

Reinforcement area | 1805 | 0.30 | 21.0 | 200 | 28 |

Grouting steel pipe | 76,225 | 0.20 | 28.4 | ||

Concrete | 28,000 | 0.20 | 23.0 | ||

I-steel | 210,000 | 0.30 | 78.5 |

Positions | Maximum/mm | Final Values/mm | Final Convergence Rates/mm·d^{−1} |
---|---|---|---|

Measuring line 1-1 | −11.5 | 1.4 | −0.1 |

Measuring line 1-2 | −8.5 | 9.2 | 0.0 |

Monitoring Points | Maximum/mm | Final Values/mm | Final Settlement Rates/mm·d^{−1} |
---|---|---|---|

D_{1} | −3.4 | 5.4 | 0.1 |

D_{2} | −9.9 | -9.9 | 0.0 |

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## Share and Cite

**MDPI and ACS Style**

Wang, K.; Xiong, Y.; Li, S.; Zhou, X.; Li, Z. Deformation Characteristics Analysis of Temporary Support in Unsymmetrical Loading Tunnel Excavation under Composite Support. *Symmetry* **2023**, *15*, 830.
https://doi.org/10.3390/sym15040830

**AMA Style**

Wang K, Xiong Y, Li S, Zhou X, Li Z. Deformation Characteristics Analysis of Temporary Support in Unsymmetrical Loading Tunnel Excavation under Composite Support. *Symmetry*. 2023; 15(4):830.
https://doi.org/10.3390/sym15040830

**Chicago/Turabian Style**

Wang, Kezhong, Yu Xiong, Sheng Li, Xin Zhou, and Zhikuan Li. 2023. "Deformation Characteristics Analysis of Temporary Support in Unsymmetrical Loading Tunnel Excavation under Composite Support" *Symmetry* 15, no. 4: 830.
https://doi.org/10.3390/sym15040830