Study on Transverse Deformation Characteristics of a Shield Tunnel under Earth Pressure by Refined Finite Element Analyses
Abstract
:1. Introduction
2. Numerical Model Construction and Validation
2.1. Finite Element Model
2.2. Constitutive Model and Parameters
2.3. Interactions
2.4. Validation
3. Loading Mode and Numerical Cases
3.1. Loading Mode
3.2. Numerical Cases
4. Results and Analyses
4.1. Convergence
4.2. Joint Deformation
4.3. Rebar Stress
4.4. Bolt Stress
5. Discussions
5.1. Relationship between Convergence and Joint Opening
5.2. Relationship between Joint Opening and Bolt Stress
6. Conclusions
- (1)
- In this study, we have established a refined numerical model for the segmental lining of a shield tunnel using finite element software, which contains detailed models of the reinforcement and connecting bolts. The model parameters were validated using a full-scale model test result. The numerical calculation results highly agree with the full-scale test, which verifies the accuracy of the numerical model. We prove that the refined numerical simulation method reasonably reflects the deformation of the segmental lining and can be used in subsequent studies.
- (2)
- When the lining is deformed by earth pressure, the concrete at the joints is squeezed to produce large strains, resulting in plastic hinges forming at the joints. When the lining is deformed by earth pressure, the segment rotates around the plastic hinge, causing the joints to open. The rotation of the segment is the main reason for segmental lining deformation under earth pressure.
- (3)
- Horizontal convergence is a single index reflecting the deformation of the tunnel ring, representing the overall deformation of the ring to a certain extent but not the deformation characteristics of the joint. When loading conditions differ, the relationship between joint opening and horizontal convergence is consistent for some joints and inconsistent for others.
- (4)
- When the joint is open in the outer arc, the relationship between joint opening and bolt stress is different under different loading conditions. However, the relationship between joint opening and bolt stress is consistent when opening in the inner arc; bolt stress reaches a yield of 640 MPa, with a joint opening range of 4.50–5.50 mm.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Material | E (MPa) | ν | σ0 (MPa) | σu (MPa) |
---|---|---|---|---|
Segmental lining | 34,500 | 0.2 | 46 | 55 |
Rebar | 200,000 | 0.3 | 400 | 500 |
Bolt | 206,000 | 0.3 | 640 | 800 |
Bolt washer | 206,000 | 0.3 | — | — |
Bolt sleeve | 2000 | 0.35 | — | — |
Level | P1 (kN) | P2 (kN) | P3 (kN) | Level | P1 (kN) | P2 (kN) | P3 (kN) |
---|---|---|---|---|---|---|---|
0 | 0 | 0 | 0 | 11 | 278 | 210 | 205 |
1 | 31 | 26.4 | 26.2 | 12 | 309.2 | 228 | 231 |
2 | 62 | 52.8 | 52.4 | 13 | 340.4 | 246 | 257 |
3 | 93 | 79.2 | 78.6 | 14 | 356 | 255 | 270 |
4 | 124 | 105.6 | 104.8 | 15 | 381.4 | 272.2 | 287.6 |
5 | 155 | 132 | 131 | 16 | 406.8 | 289.4 | 305 |
6 | 187 | 152.4 | 149.4 | 17 | 432.2 | 306.6 | 322.6 |
7 | 219 | 172.8 | 167.8 | 18 | 457.6 | 323.8 | 340 |
8 | 235 | 183 | 177 | 19 | 483 | 341 | 357.6 |
9 | 252.2 | 193.8 | 188.2 | 20 | 508.4 | 358.2 | 375 |
10 | 269.4 | 204.6 | 199.4 | — | — | — | — |
Case | Pv1 (kPa) | λ | k (kPa/m) |
---|---|---|---|
C1 | 0~2000 | 0.45 | 10,000 |
C2 | 0~2000 | 0.50 | 10,000 |
C3 | 0~2000 | 0.55 | 10,000 |
C4 | 0~2000 | 0.60 | 10,000 |
C5 | 0~2000 | 0.65 | 10,000 |
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Long, W.; Chen, W.; Huang, C.; Li, D.; Su, D. Study on Transverse Deformation Characteristics of a Shield Tunnel under Earth Pressure by Refined Finite Element Analyses. Symmetry 2022, 14, 2030. https://doi.org/10.3390/sym14102030
Long W, Chen W, Huang C, Li D, Su D. Study on Transverse Deformation Characteristics of a Shield Tunnel under Earth Pressure by Refined Finite Element Analyses. Symmetry. 2022; 14(10):2030. https://doi.org/10.3390/sym14102030
Chicago/Turabian StyleLong, Wen, Weijie Chen, Changfu Huang, Dongyang Li, and Dong Su. 2022. "Study on Transverse Deformation Characteristics of a Shield Tunnel under Earth Pressure by Refined Finite Element Analyses" Symmetry 14, no. 10: 2030. https://doi.org/10.3390/sym14102030
APA StyleLong, W., Chen, W., Huang, C., Li, D., & Su, D. (2022). Study on Transverse Deformation Characteristics of a Shield Tunnel under Earth Pressure by Refined Finite Element Analyses. Symmetry, 14(10), 2030. https://doi.org/10.3390/sym14102030