Mechanical Behavior of Double-Arch Tunnels under the Effect of Voids on the Top of the Middle Wall
Abstract
:1. Introduction
2. Feasibility Study of the Extended Finite Element Method for Simulating Crack Propagation
2.1. Physical Model Test
2.1.1. Model Test Apparatus
2.1.2. Model Test Materials
2.1.3. Test Monitoring
2.1.4. Test Procedures
2.2. Numerical Analysis
2.2.1. Numerical Model
2.2.2. Model Details
2.2.3. Simulation of Voids
2.3. Comparisons between Model Test and Numerical Simulation
2.3.1. Internal Forces of the Liner
2.3.2. Deformation of the Liner
2.3.3. Failure Patterns of the Liner
3. Effects of the Void on the Top of the Middle Wall on Double-Arch Tunnels
3.1. Effects of Void Height
3.1.1. Effects of Void Height on Internal Forces
3.1.2. Effects of Void Height on the Deformation of the Liner
3.1.3. Effects of Void Height on Failure Patterns
3.2. Effects of Tunnel Shape
3.2.1. Effects of Tunnel Shape on Internal Forces
3.2.2. Effects of Tunnel Shape on the Deformation of the Liner
3.2.3. Effects of Tunnel Shape on the Failure Patterns of the Liner
4. Conclusions
- (1)
- The bottom of the middle wall suffered the greatest damage and was the key vulnerability of the structure. Cracks occurred firstly at the bottom of the middle wall whether or not the void existed, which was also consistent with the bending moment distribution.
- (2)
- Internal forces of the liner in double-arch tunnels were affected greatly by the void on the top of the middle wall. The largest changes occurred at the connection between the spandrel and the middle wall. In addition, voids on the top of the middle wall led to a larger deformation and helped to reduce the settlement of the middle wall. Furthermore, more cracks and larger concrete compression failure zones were found at the connection between the spandrel and the middle wall compared with the tunnel without voids.
- (3)
- Void height and the diameter of tunnels were key factors to determine the effects of voids on double-arch tunnels. The larger the void height, the greater the effects the void led to. Furthermore, the larger diameter tunnel in asymmetrical double-arch tunnels was more sensitive to void height changes and suffered more serious effects of the void than the smaller one.
- (4)
- Tunnel shape also played a significant role to determine the effects of voids. Unlike the asymmetrical double-arch tunnels, changes in internal forces and deformation in symmetrical double-arch tunnels were distributed symmetrically.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Parameters | Similarity Ratios |
---|---|
Over load | 40 |
Geometry | 40 |
Unit weight | 1 |
Elastic modulus | 40 |
Poisson’s ratio | 1 |
Cohesion | 40 |
Friction angle | 1 |
Materials | Unit Weight (kN/m3) | Elastic Modulus (GPa) | Poisson’s Ratio | Cohesion (kPa) | Friction Angle (°) |
---|---|---|---|---|---|
Rock mass—M 1 | 18 | 0.021 | 0.32 | 4.6 | 22 |
Rock mass—P 2 | 18 | 0.85 | 0.32 | 180 | 22 |
Liner—M | 8.4 | 0.723 | 0.20 | — | — |
Liner—P | 25 | 30 | 0.20 | — | — |
Liner for CS1 | Liner for CS2 | ||
---|---|---|---|
Test Number | Height of Voids | Test Number | Height of Voids |
CS1-1 | None | CS2-1 | None |
CS1-2 | 1.0 m | CS2-2 | 1.0 m |
CS1-3 | 2.0 m |
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Share and Cite
Min, B.; Zhang, X.; Zhang, C.; Gong, Y.; Yuan, T. Mechanical Behavior of Double-Arch Tunnels under the Effect of Voids on the Top of the Middle Wall. Symmetry 2018, 10, 703. https://doi.org/10.3390/sym10120703
Min B, Zhang X, Zhang C, Gong Y, Yuan T. Mechanical Behavior of Double-Arch Tunnels under the Effect of Voids on the Top of the Middle Wall. Symmetry. 2018; 10(12):703. https://doi.org/10.3390/sym10120703
Chicago/Turabian StyleMin, Bo, Xu Zhang, Chengping Zhang, Yanping Gong, and Tengfei Yuan. 2018. "Mechanical Behavior of Double-Arch Tunnels under the Effect of Voids on the Top of the Middle Wall" Symmetry 10, no. 12: 703. https://doi.org/10.3390/sym10120703
APA StyleMin, B., Zhang, X., Zhang, C., Gong, Y., & Yuan, T. (2018). Mechanical Behavior of Double-Arch Tunnels under the Effect of Voids on the Top of the Middle Wall. Symmetry, 10(12), 703. https://doi.org/10.3390/sym10120703