Semianalytical Analysis of Overexcavation and Critical Support Pressure for Support Design in TBM Tunneling through Squeezing Rock Condition
Publication: International Journal of Geomechanics
Volume 21, Issue 7
Abstract
Support damage is a typical hazard scenario associated with tunnel boring machine (TBM) drives in the squeezing rock condition. The stress release of the rock mass and the improvement of the support capacity are two effective methods to prevent support damage. The stress in the rock mass can be released by allowing a certain amount of overexcavation. The support capacity can be evaluated by solving the required support pressures corresponding to different critical strain levels. This paper aims to achieve a better understanding of preventing support damage for TBMs in the squeezing condition by quantitatively analyzing the overexcavation and the required support pressure. A semianalytical solution of the ground reaction curve is obtained. A simplified method of solving the support pressure with specific rock displacement is proposed. Based on the two solutions, the procedures for solving for the overexcavation and the critical support pressure are presented. Corresponding to the critical strain levels of 1%, 2.5%, 5%, and 10%, the response surfaces for critical support pressures in relation to the Geological Survey Index (GSI) and in situ stress are obtained via the nonlinear regression method. The influences of GSI, in situ stress, and the mechanical parameters of the concrete lining and shield on the size of the overexcavation are comprehensively investigated. A method to guide support design in the squeezing rock mass is proposed. Three tunnel cases are presented to demonstrate the application of the method, and three case histories that encounter support failures are discussed to illustrate the appropriate design measures through the proposed method.
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Acknowledgments
The authors acknowledge the financial support provided by National Natural Science Foundation of China (Grant Nos. 52009129, 51909248, and 51909259), Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering (Grant No. 201704), and Open Research Fund of State Key Laboratory of Coastal and Offshore Engineering (Grant No. LP2012).
Notation
The following symbols are used in this paper:
- E1
- elastic modulus of the shield;
- E2
- elastic modulus of the concrete lining;
- Er
- elastic modulus of the rock mass;
- f
- failure criterion;
- f0
- displacement reduction ratio;
- g
- flow potential;
- K1
- stiffness of the shield;
- K2
- stiffness of the concrete lining;
- Kψ
- dilatancy coefficient;
- mb, s, a
- strength constants in the Hoek-Brown failure criterion;
- n
- number of annuli in the plastic zone by the finite difference method;
- pi
- support pressure;
- pi,1
- contacting pressure between the shield and the rock mass;
- pi,cri1
- required critical support pressure corresponding to ɛi,cri1 = 1%;
- pi,cri2
- required critical support pressure corresponding to ɛi,cri2 = 2.5%;
- pi,cri3
- required critical support pressure corresponding to ɛi,cri3 = 5.0%;
- pi,cri4
- required critical support pressure corresponding to ɛi,cri4 = 10%;
- pi,fic
- fictitious support pressure added on the tunnel periphery;
- pi,fin
- contacting pressure between the concrete lining and the rock mass;
- pi,max
- maximum capacity of the support;
- R
- location of the rock mass to the center of the circular opening;
- R*
- normalized plastic radius;
- R0
- radius of the circular opening;
- Rp
- radius of the plastic zone;
- maximum plastic radius;
- r(i)
- radial distance to the center of a circular opening at the inner boundary of the ith annulus;
- t1
- thickness of the shield;
- t2
- thickness of the shotcrete;
- u
- radial displacement;
- u0
- radial displacement at the tunnel periphery;
- u0,1
- rock displacement at the tunnel periphery when the rock mass and the shield reach an equilibrium;
- u0,fin
- rock displacement at the tunnel periphery when the rock mass and the concrete lining reach an equilibrium;
- u0,fin1
- u0,fin solved by the FDM analysis;
- u0,fin2
- u0,fin solved by the proposed solution;
- u0,ini
- initial radial displacement at the tunnel face;
- u0,max
- maximum radial displacement;
- ur(i)
- radial displacement at r = r(i);
- Δr
- radial increment in the plastic zone;
- ΔR0
- size of the overexcavation;
- Δt1
- deformation of the shield;
- Δt2
- deformation of the lining;
- ɛr
- radial strain;
- elastic radial strain;
- plastic radial strain;
- ɛθ
- tangential strain;
- ɛθ(i)
- tangential strain at r = r(i);
- ɛθ,cri1
- critical strain level of 1%;
- ɛθ,cri2
- critical strain level of 2.5%;
- ɛθ,cri3
- critical strain level of 5%;
- ɛθ,cri4
- critical strain level of 10%;
- ɛθ,fin
- tunnel strain corresponding to u0,fin, ɛθ,fin = u0,fin/R0;
- ɛθ,ini
- tunnel strain corresponding to u0,ini, ɛθ,ini = u0,ini/R0;
- elastic tangential strain;
- plastic tangential strain;
- μ1
- Poisson's ratio of the shield;
- μ2
- Poisson's ratio of the concrete lining;
- σ0
- in situ stress field;
- σ1
- major principal stress;
- σ3
- minor principal stress;
- σc,max
- compressive strength of the concrete lining;
- σci
- compressive strength of the intact rock;
- σcm
- compressive strength of the rock mass;
- σr
- radial stress of the rock mass;
- σr2
- radial stress at the elastoplastic boundary;
- σθ
- tangential stress of the rock mass; and
- ψ
- dilatancy angle.
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Received: Jun 27, 2020
Accepted: Jan 17, 2021
Published online: Apr 21, 2021
Published in print: Jul 1, 2021
Discussion open until: Sep 21, 2021
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