Abstract
The face stability assessments of seismic tunnels have been complicated and crucial problems. To solve this issue, an advanced three-dimensional (3D) rotational failure mechanism with considering seismic effects is developed to assess the seismic face stability of shield tunnels in weak rock masses. The Hoek-Brown (HB) failure criteria is employed to characterize rock masses with weak strength. The corresponding Mohr-Coulomb (MC) parameters are determined using the tangential line method. The modified pseudo-dynamic (MPD) approach is utilized to accurately involve damping property of geomaterials, realistic surface boundary conditions and dynamic properties of seismic waves in face stability assessments. The upper limit analysis approach is utilized for the determination of critical face pressures of seismic tunnels. Comparisons against numerical and analytical solutions demonstrate the efficacy of proposed approach for evaluating the seismic face stability. Subsequently, the impacts of seismic actions and weak rock parameters on face stability are analyzed and a design table is provided for practical use. Finally, the proposed approach is tested by conducting seismic face stability assessments of the JinXiu tunnel with actual seismic response.
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Abbreviations
- A, B and E :
-
The tunnel crown, invert, face center
- A j, A j+1, A′j, and A′j+1 :
-
Horizontal symmetry points on tunnel face
- a h0 :
-
Initial horizontal seismic acceleration at tunnel foundation
- C :
-
Cover depth
- c t :
-
Equivalent cohesion
- C j and C j+1 :
-
The center of the radial plane ΨJ, ΨJ+1
- C s, C sz, S s, S sz, q s1, q s2, C p, S p, C pz, S pz, q p1 and q p2 :
-
Dimensionless functions
- D :
-
Tunnel diameter
- D i :
-
Disturbance coefficient
- E :
-
Young’s modulus
- F :
-
Failure mechanism endpoint
- f :
-
Amplification factor of seismic wave
- f n+1 :
-
Fundamental frequency
- g :
-
Gravity acceleration
- GSI :
-
Geological strength index
- H :
-
Height between ground and tunnel foundation
- HB :
-
Hoek-Brown
- k h, and k v :
-
The horizontal and vertical seismic coefficients
- MC :
-
Mohr-Coulomb
- m i :
-
Constant HB parameters
- MPD :
-
Modified pseudo-dynamic
- N γ N D, N sh and N sv :
-
Dimensionless coefficients
- O :
-
Rotational center O of rotational failure mechanism
- PD :
-
Pseudo-dynamic
- P i,j, P i+1, P i,j+1 and P i+1,j+1 :
-
Points at the failure surface
- PS :
-
Pseudo-static
- r A, r B, r E and r F :
-
Rotation radius of points PA, PB, PE and PF
- r F, b F :
-
Rotational radius and the rotational angle of the point F
- R i,j and R i,j :
-
Polar radius of projected area barycenter Si,j and S′i,j
- R j and b j :
-
Polar coordinates of the discretized element
- S i,j and S′i,j :
-
Projected area onto the symmetric plane of lower triangular element and upper triangular element
- T :
-
Seismic wave period
- t :
-
Time
- u h(y, t) and u v(y, t):
-
Horizontal and vertical displacement at depth y and time t
- u ho and u vo :
-
Horizontal and vertical displacements at tunnel foundation
- v :
-
Linear velocity
- V i,j, V i,j :
-
Volumes of lower and upper triangular elements
- V p and V s :
-
Primary and shear wave velocities
- W D :
-
Internal energy dissipation rates
- W sh and W sv :
-
Horizontal and vertical seismic working rates
- W γ :
-
Working rates induced by rock weight
- W σT :
-
Working rates of supporting forces
- y i,j and y′i,j :
-
The y-coordinate of the barycenter of projected area Si,j and S′i,j
- β A, β B, β E and β F :
-
Angles between lines OA, OB, OE, and OF in relation to the vertical direction
- β i,j and β′i,j :
-
Barycenter polar angle of the projected area Si,j and S′i,j
- γ :
-
Unit rock weight
- φ t :
-
Equivalent friction angle
- κ, s, and μ :
-
Material variables of weak rock
- ν:
-
Poisson’s ratio
- Σj :
-
Discretized element area of tunnel face
- σ 1 :
-
Major principal stresses
- σ 3 :
-
Minor principal stresses
- σ c :
-
Uniaxial compressive strength
- σ n :
-
Normal stress
- σ T :
-
Critical face pressure
- τ :
-
Shear stress
- \(\varpi \) :
-
Angular velocity
- ω :
-
Angular frequency
- ξ :
-
Damping ratio
- Ψ A, Ψ B, and Ψ F :
-
Radial plane of the failure mechanism through points A, B, and F.
- Ψ j and Ψ j+1 :
-
Radial plane of the failure mechanism
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Acknowledgements
The support from the National Key R&D Program of China (2017YFB1201204) is greatly appreciated. The support from the Guizhou Provincial Science and Technology Major Project (Qian-ke-he-zhong-da-zhuan-xiang-zi [2018]3010) is also greatly appreciated.
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Zou, J., Li, S. & Chen, G. Three-Dimensional Face Stability Assessments of Seismic Tunnels in Weak Rock Masses. KSCE J Civ Eng 28, 2469–2485 (2024). https://doi.org/10.1007/s12205-024-1887-5
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DOI: https://doi.org/10.1007/s12205-024-1887-5