Abstract
The ConVergence-ConFinement (CV-CF) method is widely used in conventional tunneling at a preliminary stage of the design. In this method, the rock–support interaction is simplified by means of a two-dimensional plane-strain assumption. However, when the ground exhibits large deformation and/or when the support is very stiff and installed close to the tunnel face, the results obtained with the CV-CF method may significantly differ from those obtained using 3D numerical computations. The strong interaction taking place between the rigid lining and the rock mass is not considered in the most common use of the CV-CF method. Some improvements of the CV-CF method as the so-called implicit methods have been developed to better account for this interaction. In this paper, the applicability of the CV-CF methods is discussed for full-face excavation tunneling with a stiff support system. An in-depth comparison between plane-strain closed form solutions and numerical results which properly accounts for the 3D effects at the vicinity of the tunnel face is carried out. The range of application of the different approaches of the CV-CF method is discussed. Finally, some simple empirical formulae which can be used in preliminary design for a large range of ground conditions are proposed.
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Abbreviations
- \(x\) :
-
Distance to the tunnel face
- \(R\) :
-
Tunnel radius
- \(D\) :
-
Tunnel diameter
- \(d\) :
-
Distance of support/lining installation from the tunnel face
- \({x_{\text{f}}}\) :
-
Distance between the edge of the lining and the tunnel face (unsupported length)
- \(s\) :
-
Step round length in the numerical simulations
- \(e\) :
-
Thickness of the support or the lining
- \({R}_{o}\) :
-
Outer radius of a lining
- \({R_{\text{i}}}\) :
-
Inner radius of a lining
- \(\lambda \left(x\right)\) :
-
Deconfining rate which depends on the distance to the advancing face x
- \(c\) :
-
Cohesion of the ground
- ϕ:
-
Friction angle of the ground
- \(\psi\) :
-
Dilatancy angle of the ground
- \({K_{\text{p}}}\) :
-
Friction parameter of the ground
- \(\beta\) :
-
Dilatancy parameter of the ground
- \(\upsilon\) :
-
Poisson’s ratio of the ground
- \(E\) :
-
Young’s modulus of the ground
- \(G\) :
-
Shear modulus of the ground
- \({\upsilon _{\text{l}}}\) :
-
Poisson’s ratio of the support or the lining
- \({E_{\text{l}}}\) :
-
Young’s modulus of the support or the lining
- \({G_{\text{l}}}\) :
-
Shear modulus of the support or the lining
- \(N\) :
-
Stability number
- \({R_{{\text{pl}}}}\) :
-
Plastic radius (unsupported opening)
- \({k_{{\text{sn}}}}\) :
-
Normal stiffness of the support
- \({K_{{\text{sn}}}}\) :
-
Normal stiffness of a lining
- \(u\left( x \right)\) :
-
Radial displacement at the tunnel wall which depends on the distance to the advancing face \(x\) (unsupported opening)
- \(\bar {u}\left( x \right)\) :
-
Radial displacement at the tunnel wall which depends on the distance to the advancing face \(x\) (supported opening)
- \({p_{\text{f}}}\) :
-
Fictitious pressure applied to the tunnel boundary (to account for the influence of the tunnel face)
- \({\sigma _0}\) :
-
Initial isotropic stress state in the ground
- \({\sigma _{\text{c}}}\) :
-
Uniaxial compression strength
- \({p_{\text{s}}}\) :
-
Radial pressure acting upon the outer boundary of the lining
- \({\sigma _{\text{max}}}\) :
-
Maximal hoop stress developed in the support or the lining at the state of equilibrium
- \(\chi\) :
-
Homothetic ratio in the Self Similarity Principle
- \(\ldots {,^*}\) :
-
Normalized parameter/variable
- \(\ldots ,{~_{{\text{el}}}}\) :
-
Elastic parameter/variable
- \(\ldots ,{~_{{\text{pl}}}}\) :
-
Elastoplastic parameter/variable
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Acknowledgements
This work is part of the Ph.D. thesis of the first author, carried out at Ecole des Ponts ParisTech in partnership with Tractebel ENGIE and CETU (Centre d’Études des Tunnels). The authors wish to thank ITASCA for supporting the first author through the Itasca Education Partnership Program (IEPP).
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Appendix: CV-CF Methods for Double-Shield TBM
Appendix: CV-CF Methods for Double-Shield TBM
In an attempt to assess the applicability of the CV-CF methods to tunnels excavated with a double-shield TBM, some numerical simulations have been carried out by fixing the value of the parameter \({d^{\text{*}}}\) to 2. The results are summarized in Figs. 12 and 13. It is inferred from the results that a classical CV-CF method in combination with the LDP of Panet provides an equilibrium state which is in agreement with the numerical simulations if \({E^*}\) > 0.25. The effect of the stiffness of the lining on the GRC is less than in the case of single-shield tunneling. The implicit method of Guo and Minh combined with an LDP of Panet provides also reasonable results except for N = 5 where the implicit method reaches its limits (N = 5 and \({d^{\text{*}}}\) = 2).
Comparison of \({\sigma _{\text{max}}}^{*}\) between the different approaches when \({d^{\text{*}}}\) = 2, \({R^*}\) = 12.5, and \(\phi\) = 20° for incompressible plasticity (\(\psi\) = 0). Classical method on the left column and implicit method of Nguyen-Minh and Guo on the right column
Comparison of \(\bar {u}{\left( \infty \right)^*}\) between the different approaches when \({d^{\text{*}}}\) = 2, \({R^*}\) = 12.5, and \(\phi\) = 25° for incompressible plasticity (\(\psi\) = 0). Classical method on the left column and implicit method of Nguyen-Minh and Guo on the right column
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De La Fuente, M., Taherzadeh, R., Sulem, J. et al. Applicability of the Convergence-Confinement Method to Full-Face Excavation of Circular Tunnels with Stiff Support System. Rock Mech Rock Eng 52, 2361–2376 (2019). https://doi.org/10.1007/s00603-018-1694-8
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DOI: https://doi.org/10.1007/s00603-018-1694-8