Abstract
The instabilities of tunnel face may occur while shields advance through the rivers or region rich in water. It is of significance to attach the importance to the estimation of face stability during the tunnel excavation. Thus, this paper adopted a three-dimensional (3D) rotational mechanism to analyze the face stability under steady seepage flow field with the aid of the kinematic method in the context of limit analysis. The hydraulic head that derived by fitting the results of trial and error is employed herein to portray the steady seepage flow field. With the aid of a double integration method, the work rate induced by seepage forces acting on the soil skeleton is calculated and accordingly a closed-form solution of support pressure is derived based on the work balance equation. By comparing with the literature, one can validate the rationality and correctness of the present results. The research shows that the proposed method based on rotational mechanism provides a better upper bound estimation, when under seepage condition, the influence of internal frictional angle on the stability of the excavation face is not always monotonic and the influence of head difference on the support pressure is significant. Finally, the normalized stability charts are provided for a quick assessment for practical use during tunnel excavation in water-rich stratum.
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Abbreviations
- c′:
-
Effective cohesion of soils
- D :
-
Energy dissipated in the sliding surface
- d :
-
Diameter of tunnel face
- dz :
-
Thickness of single layer
- f x :
-
Unit volume seepage force along x — coordinate
- f y :
-
Unit volume seepage force along y — coordinate
- f z :
-
Unit volume seepage force along z — coordinate
- h 0 :
-
Elevation of undisturbed water table
- h F :
-
Hydraulic head on the tunnel face
- k 1 :
-
Coefficient in Eq. (2)
- k 2 :
-
Coefficient in Eq. (3)
- l(α):
-
Length of strip element at α
- N c :
-
Dimensionless coefficient induced by cohesion
- N s :
-
Dimensionless coefficient induced by support pressure
- N y :
-
Dimensionless coefficient induced by soil weight
- R :
-
Radius of circles of rotational mechanism
- r m :
-
Distance between circle center and rotation center
- r p :
-
Length of line OP
- r′:
-
Length of line OP′
- s′:
-
Effective support pressure on tunnel face
- t :
-
Overburden
- W s′ :
-
Work rate done by support pressure
- W s1 W s2 :
-
Work rate result from seepage force
- W γ′ :
-
Work rate done by soil weight
- x :
-
Horizontal coordinate in the advanced direction
- y :
-
Horizontal coordinate perpendicular to x
- z :
-
Vertical coordinate
- α :
-
Polar angle of strip element
- γ′:
-
Buoyancy weight of soils
- γ sat :
-
Saturated unit weight of soils
- γ w :
-
Unit weight of water
- Δh :
-
hF−h0
- θ′:
-
Inclined angle of OP′ and x-coordinate
- θ :
-
Inclined angle of OP and x-coordinate
- θ A :
-
Angle between line OA and horizontal direction
- θ B :
-
Inclined angle of OB and x-coordinate
- θ E :
-
Inclined angle of OE and x-coordinate
- ϕ′:
-
Effective friction angle of soils
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This work was supported by CSU (2020zzts642), which is greatly appreciated.
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Zhong, JH., Liao, H. Stability Analysis of 3D Deep Tunnel Face under Steady Seepage Flow Condition. KSCE J Civ Eng 26, 2509–2518 (2022). https://doi.org/10.1007/s12205-022-1907-2
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DOI: https://doi.org/10.1007/s12205-022-1907-2