Face Stability Of Circular Tunnel Research Articles

Numerical analyses for three-dimensional face stability of circular tunnels in purely cohesive soils with linearly increasing strength

The tunnel face stability in purely cohesive soils with linearly increasing strength was investigated using three-dimensional finite element limit analysis (FELA). Both the collapse (active failure) and blow-out (passive failure) of the tunnel face were considered in the analysis. The rigorous upper bound (UB) and lower bound (LB) solutions of the load factor were calculated with a wide range of ground conditions to cover a broad scope of practical application. The results showed that the whole surface of the face is at failure in the collapse case; while in the blow-out case, there exists a gradual evolution process from partial failure to global failure within the tunnel face with increasing buried depth. Later, based on 960 finite element limit analysis results, a series of practical equations were proposed for tunnel face stability analysis in purely cohesive soils. These equations can be employed to quickly calculate the UB and LB solutions of the limit support pressure and the stability number of a tunnel face in both the collapse and blow-out cases. Finally, the calculation results from these equations were compared with those from previous studies in detail. The comparisons showed that the proposed equations make an improvement over existing methods and can be used as an efficient tool in practical engineering.

Revisiting the face stability of circular tunnels driven in strength nonlinearity soils

The face stability of shield-driven tunnels in soil materials with distinct strength nonlinearity is re-evaluated, based on the kinematic limit analysis theorem. The nonlinear Power-Law failure criterion is piecewise approximated by a multi-tangent technique to improve the conventional single straight-line substitution. A new multi-cone rotational mechanism formed by n curvilinear cones is proposed to accommodate the nonlinearity of the strength envelope considering the associative flow rule. The analytical solution of the critical support pressure on tunnel faces is derived from the energy equilibrium equation. Calculation results show that the multi-tangent method can improve the calculated values by up to 20% compared to the generalized tangent method. According to the back-calculated stress vectors, it is interestingly found that the stress level is not the critical factor influencing the tunnel face stability, while the shear strength parameters are the direct factor. Although the upper-bound analysis is a kinematic method without involving stress analysis, the parametric form of the strength criterion gives a chance to infer the possible stress distribution on the rupture surface and explain the variational trend of the result based on the distribution of back-calculated stress vectors.

Three-dimensional undrained face stability of circular tunnels in non-homogeneous and anisotropic clays

The advanced 3D finite element limit analysis is employed to examine three-dimensional (3D) face stability of circular tunnels in undrained clays with the impact of strength non-homogeneity and anisotropy. The soil behaviour for all analyses is governed by the anisotropic undrained shear (AUS) strength model, which requires three anisotropic undrained shear strengths that are simply evaluated from conventional laboratory tests. The upper and lower bound solutions of 3D face stability of circular tunnels are accurately analyzed by considering four dimensionless parameters, including the cover-to-depth ratio, the overburden stress factor, the strength gradient ratio, and the anisotropic strength ratio. The significance of four dimensionless parameters on the stability load factor of the 3D face stability of circular tunnels, and the predicted failure mechanisms due to the influence of cover depth ratios, are also illustrated. A nonlinear regression analysis is employed to the computed data, which enables a new design equation of the factor of safety incorporating the conventional stability number. Thus, the new tunnel stability factors are proposed for the first time in the literature. A comprehensive application of the proposed safety factor equation is also presented and compared. The 3D effects of the tunnel face configuration between 3D geometry and 2D plane strain heading on the tunnel stability factors are also discussed. The new proposed design equation of the factor of safety provides an accurate and practical tool in assessing face stability of circular tunnels in non-homogeneous and anisotropic clays.

A 3D rotational silo-torus model for face stability analysis of circular tunnels

To avoid tunnel collapse during construction, a critical support pressure needs to be determined and applied on the tunnel face. This paper presents the development of a new 3D limit equilibrium model including geometries of a lower torus and an upper silo. The torus geometry was derived using a newly developed spatial discretization technique and subdivided by a wedge slice scheme. The critical support pressure was determined iteratively using the equations given in this paper. The model adopted different lateral stress coefficients for the silo and the torus geometry under different arching levels. The interface behaviour was also considered between the sliding torus and the surrounding soils. Validating with centrifuge tests, analytical and numerical tests demonstrated the accuracy of the proposed 3D model which is based on a realistic side rotational mechanism. The shear force distribution on the rotational surface was presented at the state of limit equilibrium. Finally, the effects of geotechnical and geometrical parameters (c’, φ’ and Tm) were discussed on the face stability of circular tunnels.

Effect of Longitudinal Gradient on 3D Face Stability of Circular Tunnel in Undrained Clay

The longitudinal gradient existed in shield-driven tunnel crossing river or channel has a longitudinal gradient, which is often ignored in most stability analyses of the tunnel face. Considering the influence of the longitudinal gradient into A(a) continuous velocity field, the present paper, conducting a limit analysis of the tunnel face in undrained clay, adopted to yield the upper-bound solutions of the limit pressure supporting on a three-dimensional tunnel face. The least upper bounds of the collapse and blow-out pressures can be obtained by conducting an optimization procedure. These upper-bound solutions are given in the design charts, which provide a simple way to assess the range of the limit pressure in practice. The influence of the longitudinal gradient becomes more significant with the increase of γD/su and C/D. The blow-out pressure for tunneling in a downward movement could be overestimated and the collapse pressure for tunneling in an upward movement could be conversely underestimated, with ignoring the influence of the longitudinal gradient.

Discussion of “Using a Pressurized Shield to Increase Face Stability of Circular Tunnels in Purely Cohesive Soil” by Wantao Ding, Shucai Li, Keqi Liu, Jian Zhu, Mingjiang Li, and Peihe Shi

Discussion of “Using a Pressurized Shield to Increase Face Stability of Circular Tunnels in Purely Cohesive Soil” by Wantao Ding, Shucai Li, Keqi Liu, Jian Zhu, Mingjiang Li, and Peihe Shi

Closure to “Using a Pressurized Shield to Increase Face Stability of Circular Tunnels in Purely Cohesive Soil” by Wantao Ding, Shucai Li, Keqi Liu, Jian Zhu, Mingjiang Li, and Peihe Shi

Closure to “Using a Pressurized Shield to Increase Face Stability of Circular Tunnels in Purely Cohesive Soil” by Wantao Ding, Shucai Li, Keqi Liu, Jian Zhu, Mingjiang Li, and Peihe Shi

Upper-bound solutions for face stability of circular tunnels in undrained clays

Upper-bound solutions for face stability of circular tunnels in undrained clays

Face stability analysis of shallow circular tunnels driven by a pressurized shield in purely cohesive soils under undrained conditions

Based on the slip line and limit analysis theories, this paper presents a new 3D collapse mechanism to analyze the face stability of a circular shield-driven tunnel in purely cohesive soil. The new collapse mechanism is a 4-variable multizone mechanism that depends on cover-to-diameter ratios (C/D). The proposed mechanism suggests that failure zones at the tunnel face are primarily formed by shear failure. A comparison of this approach with numerical methods and other kinematic approaches shows that the proposed failure mechanism significantly improves the existing upper-bound solutions for the face stability of circular tunnels in purely cohesive soils.

Upper-bound solutions for face stability of circular tunnel in purely cohesive soil using continuous rotational velocity field

This paper presents a 2D analysis model based on limit analysis and slip-line theories for the face stability of a circular tunnel in purely cohesive soil. The analysis model depends on the ratio of cover depth C to tunnel diameter D. When C/D is equal to 0.5, the mechanism consists of three blocks, namely, Zone I, Zone II, and Zone III. When C/D is greater than 0.5, the mechanism consists of four blocks, namely, Zone I, Zone II, Zone III, and a possible Zone IV. Zone II is a transition zone satisfying the normality conditions. The possible Zone IV is a Rankine zone that is subjected to the influence of the vertical soil arching effect appearing at the top of Zone III. The criterion for the collapse thickness limit of the tunnel is proposed based on Terzaghi’s theory of relative soil pressure. The results show that significant improvements have been made to the existing solutions using the proposed failure mechanism for the face stability of circular tunnels in purely cohesive soil.

Using a Pressurized Shield to Increase Face Stability of Circular Tunnels in Purely Cohesive Soil

AbstractTo obtain the critical collapse pressure of a circular tunnel driven by a pressurized shield for purely cohesive soils, a two-dimensional analysis model is presented based on limit analysis...

Upper bound solutions for face stability of circular tunnels in non-homogeneous and anisotropic clays

This paper presents a three-dimensional stability analysis of a circular tunnel face in non-homogeneous and anisotropic undrained clay using the kinematic approach (upper bound) of limit analysis. The proposed failure mechanism consists of a cylindrical rigid block and a toroidal shear zone with variable radius, and the closed-form analytical expressions of velocity field are derived within the framework of an orthogonal curvilinear coordinate system. The critical collapse-supporting pressure and stability ratio are obtained through optimization with respect to the geometrical parameters of the mechanism. Two types of non-homogeneous undrained strength, linearly changing with depth, and two-layer clays with constant undrained strength are investigated. Meanwhile, the 3-D finite element analysis is employed to validate the proposed failure mechanism. The upper bound solutions of the stability ratio of the proposed mechanism compare reasonably well with the upper bound solutions from the finite element analysis and show significant improvements over the existing upper bound solutions in single layer clays with homogeneous and isotropic undrained strength. The results show that the critical collapse pressure decreases with the increase in the non-homogeneous ratio and the anisotropic ratio and increases with the ratio between the undrained strength of the top layer and of the bottom layer.

Upper-bound solutions for face stability of circular tunnels in undrained clays

The aim of this paper is to determine the critical supporting pressure on the circular face of an advancing tunnel in undrained clay in which undrained strength increases linearly with depth. Based on the kinematic approach of limit analysis, a continuous velocity field with a toric envelope is adopted to yield upper bounds of the face pressure for both collapse and blow-out. Combining with a closed-form expression describing the overall velocity field, an optimisation procedure is carried out to find the lowest upper-bound solutions. The calculated results are presented in terms of a dimensionless coefficient N (called the stability number) and then stability charts for use are produced. Alternatively, an approximation formula is given to estimate easily the collapse and blow-out pressure in practice.