Seismic Stability of Circular Tunnels in Anisotropic Granular Soil with Surcharge Loading Based on the Modified Pseudodynamic Approach
Publication: International Journal of Geomechanics
Volume 24, Issue 5
Abstract
This study evaluated the stability of circular tunnels constructed in anisotropic granular soil in the presence of surcharges on the ground surface and seismic loads. The stability problem was solved using the lower bound limit analysis method in conjunction with the finite-element technique. In addition, the modified pseudodynamic technique was employed, which permits seismic accelerations to vary with depth and time, including the impact of amplitude and phase differences between shear and primary waves. The forces exerted by the soil on the tunnel lining vary over the perimeter. Therefore, the ultimate support pressure should at least be equal to the maximum normal stress from the earth surrounding the tunnel. It was discovered that parameters such as the tunnel cover depth, tunnel diameter, magnitude of surcharge, soil friction angle and its degree of anisotropy, seismic acceleration coefficients, period, and frequency of seismic waves determine the support pressure’s magnitude and location. The influence of surcharge diminished beyond a certain cover depth and diameter ratio for given soil and seismic wave parameter magnitudes. This study showed that the maximum normal stress was 8.5 times greater than the uniform stress distribution. Furthermore, the support pressure was found to be a maximum of about 45.5% higher for a tunnel cover depth-to-diameter ratio of 3 than for 1%, 34% higher for anisotropy than for isotropic case, 25% higher in the presence of ground surcharge than its absence, and 60% higher for the horizontal acceleration coefficient of 0.3 compared to the static case.
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Data Availability Statement
All data, models, and codes generated or used during the study appear in the published article.
Acknowledgments
The authors gratefully acknowledge the High-Performance Computing (HPC) facility available at the Indian Institute of Technology Kanpur for obtaining the numerical solutions.
Notation
The following symbols are used in this paper:
- ah (z, t)
- horizontal acceleration as a function of depth z and time t;
- av (z, t)
- vertical acceleration as a function of depth z and time t;
- C
- cover depth of the tunnel;
- ca
- adhesion at the soil-lining interface;
- D
- diameter of the tunnel;
- E
- Young’s modulus of the tunnel lining material;
- fah
- acceleration ratio for shear wave;
- fav
- acceleration ratio for primary wave;
- G
- shear modulus at any strain level;
- G0
- small strain shear modulus;
- g
- acceleration due to gravity;
- H
- depth from the ground surface to the bedrock;
- kh
- horizontal acceleration coefficient;
- kv
- vertical acceleration coefficient;
- m
- anisotropy coefficient;
- q
- magnitude of surcharge;
- T
- period of shaking of the seismic wave;
- t
- time;
- tl
- thickness of tunnel lining;
- Vs
- wave propagation velocity of the shear wave;
- Vp
- wave propagation velocity of the primary wave;
- z
- depth from the ground surface;
- δc
- allowable change in the thickness of tunnel lining;
- γ
- unit weight of soil;
- γs
- shear strain;
- νl
- Poisson’s ratio of the tunnel lining material;
- ξs
- damping ratio for shear wave;
- ξp
- damping ratios for primary wave;
- σn
- normal stress;
- σs
- support pressure based on the nonuniform distribution of stresses;
- σu
- support pressure based on the uniform distribution of stresses;
- τ
- shear stress;
- ϕ
- equivalent friction angle;
- ϕ1
- maximum friction angle;
- ωs
- circular frequency of shear wave; and
- ωp
- circular frequencies of the primary wave.
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Published In
International Journal of Geomechanics
Volume 24 • Issue 5 • May 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Jun 7, 2023
Accepted: Oct 21, 2023
Published online: Feb 19, 2024
Published in print: May 1, 2024
Discussion open until: Jul 19, 2024
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