Analytical Model of Mechanical Responses of Circular Tunnels Considering Rheological Behavior of Surrounding Rock and Functionally Graded Lining
Abstract
:1. Introduction
2. Problem Statement
- (1)
- The horizontal and vertical pressure are equal.
- (2)
- The rock mass is a homogeneous, isotropic, and viscoelastic material [10].
- (3)
- The excavation radius of the circular tunnel is R2.
- (4)
- The lining is an inhomogeneous, isotropic, and elastic material.
- (5)
- The inner and outer radii of the lining are R1 and R2, respectively.
- (6)
- The thickness of the lining is d.
- (7)
- The mechanical property (such as elastic modulus) of the lining varies only along the radial direction as a power function.
- (8)
- The inner surface of the lining is subjected to the pressure q(t) in the radial direction.
3. Analytical Model
3.1. Mechanical Analysis of Surrounding Rock
- (1)
- Unlined tunnel
- (2)
- Lined tunnel
3.2. Mechanical Analysis of Lining
3.3. Deformation Compatibility on Rock–Lining Interface
4. Validation
4.1. Comparison with Existing Analytical Solution
4.2. Comparison with Numerical Simulation
5. Parametric Analysis
5.1. Radially Inhomogeneous Coefficient of Lining
5.2. Radially Inner Surface Pressure of Lining
5.3. Lining Thickness
5.4. Relaxation Time of Maxwell Model
5.5. Retardation Time of Kelvin Model
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Unit | Value |
---|---|---|
P0 | MPa | 5.89 |
R1 | m | 3.96 (constant) |
R2 | m | 4.57 |
d | m | 0.61 |
EL0 | GPa | 16.55 |
vL | - | 0.2 |
δ | - | −0.50 (0.50) |
α | - | 0.68 |
β | - | 0.60 |
t0 | a | 0.00 |
ηm | GPa·a | 1590 |
Gm | MPa | 3447 (constant) |
tm | a | 461.27 |
ηk | GPa·a | 7.98 |
Gk | MPa | 345 (constant) |
tk | a | 23.13 |
q(τ) | MPa | 0.00 (0.10) |
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Du, J.; Zhang, X. Analytical Model of Mechanical Responses of Circular Tunnels Considering Rheological Behavior of Surrounding Rock and Functionally Graded Lining. Appl. Sci. 2024, 14, 7434. https://doi.org/10.3390/app14177434
Du J, Zhang X. Analytical Model of Mechanical Responses of Circular Tunnels Considering Rheological Behavior of Surrounding Rock and Functionally Graded Lining. Applied Sciences. 2024; 14(17):7434. https://doi.org/10.3390/app14177434
Chicago/Turabian StyleDu, Jianming, and Xuan Zhang. 2024. "Analytical Model of Mechanical Responses of Circular Tunnels Considering Rheological Behavior of Surrounding Rock and Functionally Graded Lining" Applied Sciences 14, no. 17: 7434. https://doi.org/10.3390/app14177434