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Improvement to the Convergence-Confinement Method: Inclusion of Support Installation Proximity and Stiffness

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Abstract

The convergence-confinement method (CCM) is a method that has been introduced in tunnel construction that considers the ground response to the advancing tunnel face and the interaction with installed support. One limitation of the CCM is due to the numerically or empirically driven nature of the longitudinal displacement profile and the incomplete consideration of the longitudinal arching effect that occurs during tunnelling operations as part of the face effect. In this paper, the authors address the issue associated with when the CCM is used within squeezing ground conditions at depth. Based on numerical analysis, the authors have proposed a methodology and solution to improving the CCM in order to allow for more accurate results for squeezing ground conditions for three different excavation cases involving various excavation-support increments and distances from the face to the supported front. The tunnelling methods of consideration include: tunnel boring machine, mechanical (conventional), and drill and blast.

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Abbreviations

3D:

Three dimensions

3T:

3-Noded triangles

4Q:

4-Noded quadrilaterals

8Q:

8-Noded quadrilaterals

a :

Hoek–Brown constant

A1:

Ground material A1: expected closure = 100%

A f1a :

Curve-fit variable: tunnel face displacement

A f1b :

Curve-fit variable: tunnel face displacement

A fi :

Curve-fit variable: tunnel face displacement (i denotes excavation case number)

A L :

Curve-fit variable: LDP

A La :

Curve-fit variable: LDP

A Lb :

Curve-fit variable: LDP

A oi :

Curve-fit variable: overloading (i denotes excavation case number)

B1:

Ground material B1: expected closure = 26%

B f1a :

Curve-fit variable: tunnel face displacement

B f1b :

Curve-fit variable: tunnel face displacement

B fi :

Curve-fit variable: tunnel face displacement (i denotes excavation case number)

B L :

Curve-fit variable: LDP

B La :

Curve-fit variable: LDP

B oi :

Curve-fit variable: overloading (i denotes excavation case number)

C1:

Ground material C1: expected closure = 7%

CCM:

Convergence-confinement method

C oi :

Curve-fit variable: overloading (i denotes excavation case number)

D1:

Ground material D1: expected closure = 2%

D oi :

Curve-fit variable: overloading (i denotes excavation case number)

D t :

Tunnel diameter

E1:

Ground material E1: expected closure = 1%

E i :

Intact deformation modulus

E rm :

Rock mass deformation modulus

FEM:

Finite element method

FS:

Factory of safety

GRC:

Ground reaction curve

GSI:

Geological Strength Index

k :

Support stiffness

\(k^{{\prime }}\) :

Normalized support stiffness ratio = k/Erm

LDP:

Longitudinal displacement profile

L e :

excavation step length

L u :

Unsupported span length

m :

Hoek–Brown constant

M c :

LDP curvature modifier variable

N c :

Stability number (over loading pressure) for rock masses (2Po/σcm or 2\(\sigma_{\text{cm}}^{*}\))

\(P^{{\prime }}\) :

Normalized stress overload

\(P^{*}\) :

Normalized stress = Pi/Po

P i :

Internal pressure

P imin :

Minimum internal pressure before detrimental loosening

P o :

In situ stress condition

\(R^{*}\) :

Normalized plastic radius ratio = Rpmax/Rt

\(R_{\text{f}}^{*}\) :

Normalized reduction of final plastic radius ratio = Rpmax/Rpmaxsup

R pmax :

Maximum plastic radius, unsupported

R pmaxsup :

Maximum plastic radius, supported

R t :

Tunnel radius

S :

Hoek–Brown constant

S1:

Support class S1: FS = 1.1

SRC:

Support reaction curve

TBM:

Tunnel boring machine

u :

Tunnel displacement

\(u^{*}\) :

Normalized tunnel displacement = u/umax

\(u_{ \sup }^{*}\) :

Normalized supported tunnel displacement = u/umaxsup

u maxsup :

Maximum supported displacement

\(u_{\text{f}}^{*}\) :

Normalized final tunnel displacement ratio = umax/umaxsup

\(u_{\text{fo}}^{*}\) :

Normalized final face displacement = uo/uosup

u max :

Tunnel max displacement, unsupported

u maxsup :

Tunnel max displacement, supported

u o :

Tunnel displacement at the face cross section, unsupported

\(u_{\text{o}}^{*}\) :

Normalized face displacement = uo/umax

u osup :

Tunnel displacement at the face cross section, supported

\(u_{\text{osup}}^{*}\) :

Normalized tunnel displacement at the face cross section, supported = uosup/umaxsup

\(X^{*}\) :

Normalized distance from the face = X/Rt

X :

Distance from tunnel face

ν :

Poisson’s ratio

σ ci :

Uniaxial compressive strength of the intact rock

σ cm :

Uniaxial compressive strength of the rock mass

\(\sigma_{{_{\text{cm}} }}^{*}\) :

Normalized rock mass strength ratio = Po/σcm

σ L :

Longitudinal stress

σ r :

Radial stress

σ t :

Tangential stress

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Acknowledgements

This work has been supported by funds from the Natural Sciences and Engineering Research Council of Canada, the Department of National Defence (Canada), as well as graduate funding obtained at Queen’s University and the Royal Military College of Canada. Special thanks go to Dr. Gabe Walton for his help with the data analysis use of MATLAB as well as Mr. Ioannis Vazaios for his numerous discussions and insights into this topic.

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Oke, J., Vlachopoulos, N. & Diederichs, M. Improvement to the Convergence-Confinement Method: Inclusion of Support Installation Proximity and Stiffness. Rock Mech Rock Eng 51, 1495–1519 (2018). https://doi.org/10.1007/s00603-018-1418-0

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