Skip to main content
SpringerLink
Log in

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

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25

Similar content being viewed by others

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

References

  • AFTES-groupe de travail numerio 7 (1983) Recommendation sur l’emploi de la methode convergence-confinement. Dans Tunnels et ouvrages souterrains, vol 59, pp 218–238

  • Alejano L (2010) Why the convergence confinement method is not much used in practice. Rock Mech Civil Environ Eng 347–350

  • Barlow J (1986) Interpretation of tunnel convergence measurements. University of Alberta, Edmonton

    Google Scholar 

  • Bernaud D, Rousset G (1996) The new implicit method for tunnel analysis. Int J Numer Anal Methods Geomech 20:673–690

    Article  Google Scholar 

  • Cantieni L, Anagnostou G (2009) The effect of the stress path on squeezing behavior in tunneling. Rock Mech Rock Eng 42:289–318

    Article  Google Scholar 

  • Carranza-Torres C (2004) Elasto-plastic solution of tunnel problems using the generalized form of the Hoek–Brown failure criterion. Int J Rock Mech Min Sci 41(3):480–491

    Article  Google Scholar 

  • Carranza-Torres C, Fairhurst C (2000) Application of convergence-confinement method of tunnel design to rock masses, that satisfy the Hoek–Brown failure criterion. Tunn Undergr Sp Technol 15:187–213

    Article  Google Scholar 

  • Chern J, Shiao F, Yu C (1998) An empirical safety criterion for tunnel construction. In Proceedings of the regional symposium on sedimentary rock engineering, Taipei, Taiwan, pp 222–227

  • Corbetta F, Bernaud D, Nguyen-Minh D (1991) Contribution à la méthode convergence–confinement par le principe de la similitude. Géotechnique 54:5–11

    Article  Google Scholar 

  • Duncan Fama M (1993) Numerical modeling of yield zones in weak rock. In: Hudson J (ed) Comprehensive rock engineering. Pergamon, Oxford

    Google Scholar 

  • Fenner R (1938) Untersuchungen zur erkenntnis des gebirsdruckes. Glückauf 32(74):681–695, 705–715

    Google Scholar 

  • Gercek H (2007) Poisson’s ratio values for rocks. Int J Rock Mech Min Sci 44:1–13

    Article  Google Scholar 

  • Guenot A, Panet M, Sulem J (1985) A new aspect in tunnel closure interpretation. In: Proceedings of the 26th US symposium on rock mechanics, Rapid City, pp 445–460

  • Guilloux A, Bretelle S, Bienvenue F (1996) Prise en compte des presoutenements dans le dimensionnement des tunnels. Géotechnique 76:3–16

    Article  Google Scholar 

  • Guo C (1995) Ph.D. Caleni des tunnels profonds soutenus methode stationnaire et methodes approchees. Thesis Docteur de l’Ecole Nationale des Ponts et Chaussees

  • Hoek E (2001) Big tunnels in bad rock: 2000 Terzaghi lecture. ASCE J Geotech Geoenviron Eng 127(9):726–740

    Article  Google Scholar 

  • Hoek E, Wood D, Shah S (1992) A modified Hoek–Brown criterion for jointed rock masses. In: Hudson J (ed) Proceedings of the 17th symposium on rock mechanics, Eurock’92, pp 209–213

  • Itasca Consulting Group Inc. (2009) Fast lagrangian analysis of continua in 3 dimensions, version 4. Itasca Consulting Group Inc., Minneapolis

    Google Scholar 

  • Kirsch. EG (1898) Die theorie der elastizität und die bedürfnisse der festigkeitslehre. Zeitschrift des Vereines deutscher Ingenieure 42:797–807

    Google Scholar 

  • Lunardi P (2000) The design and construction of tunnels: analysis of controlled deformation in rocks and soils. Tunnels & Tunnelling International special supplement, (ADECO-RS approach)

  • Nguyen-Minh D, Guo C (1996) Recent progress in convergence confinement method. International Society for Rock Mechanics EUROCK, Turin, pp 855–860

    Google Scholar 

  • Oke J, Vlachopoulos N, Diederichs MS (2013) Modification of the supported longitudinal displacement profile for tunnel face convergence in weak rock. In: 47th US rock mechanics/geomechanics symposium. American Rock Mechanics Association, San Francisco

  • Oke J, Vlachopoulos N, Diederichs MS (2016) Semi-analytical model for umbrella arch systems in squeezing conditions. Tunnelling Underground Space Technol 56:136–156. https://doi.org/10.1016/j.tust.2016.03.006

    Article  Google Scholar 

  • Oreste PP (1996) Radial passive rockbolting in tunnelling design with a new convergence-confinement model. Int J Rock Mech Min Sci Geomech Abstr 33:443–454

    Article  Google Scholar 

  • Pacher F (1964) Deformationsmessungen im versuchsstollen als mittel zur erforschung des gebirgsver-haltens und zur bemessung des ausbaues. Felsmechanik und Ingenieurgeologie

  • Panet M (1993) Understanding deformations in tunnels. In: Hudson J, Brown E, Fairhurst C, Hoek E (eds) Comprehensive rock engineering. Pergamon, London, pp 663–690

    Google Scholar 

  • Panet M (1995) Le calcul des tunnels par la methode convergence-confinement. Presses de l’ecole nationale de Ponts et Chausse’s, Paris

    Google Scholar 

  • Panet M, Guenot A (1982) Analysis of convergence behind the face of a tunnel. In: Proceedings, international symposium tunnelling ‘82. IMM, London, pp 197–204

  • Rabcewicz L (1973) Principles of dimensioning the supporting system for the new Austrian tunnelling method. Water Power 25:88–93

    Google Scholar 

  • Ramoni M, Anagnostou G (2010) Tunnel boring machines under squeezing conditions. Tunn Undergr Sp Technol 25:139–157

    Article  Google Scholar 

  • Ramoni M, Anagnostou G (2011) The interaction between shield, ground and tunnel Support in TBM tunnelling through squeezing ground. Rock Mech Rock Eng 44:37–61

    Article  Google Scholar 

  • Rocscience Inc. (2013). Phase2 v8. Toronto, Ontario, Canada

  • Rugarli P (2010) Structural analysis with finite elements. ICE Publishing, London

    Book  Google Scholar 

  • Sakurai S (1983) Displacement measurements associated with the design of underground opening. In: Proceedings of the international symposium. Field measurements in geomechanics, Zurich, pp 1163–1178

  • Unlu T, Gercek H (2003) Effect of Poisson’s ratio on the normalized radial displacements occurring around the face of a circular tunnel. Tunn Undergr Sp Technol 18:547–553

    Article  Google Scholar 

  • Vlachopoulos N, Diederichs M (2009) Improved longitudinal displacement profiles for convergence confinement analysis of deep tunnels. Rock Mech Rock Eng 42:131–146. https://doi.org/10.1007/s00603-009-0176-4

    Article  Google Scholar 

  • Vlachopoulos N, Diederichs MS (2014) Appropriate uses and practical limitations of 2D numerical analysis of tunnels and tunnel support response. Geotech Geol Eng 32(2):469–488. https://doi.org/10.1007/s10706-014-9727-x

    Article  Google Scholar 

  • Zhao K, Janutolo M, Barla G (2012) A completelt 3D model for the simulation of mechanized tunnel excavation. Rock Mech Rock Eng 45(4):475–497

    Article  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Mine Design Engineering, 7-1045 John Counter Blvd., Kingston, ON, K7K 6C7, Canada

    Jeffrey Oke

  2. GeoEngineering Centre at Queen’s-RMC, Kingston, ON, Canada

    Nicholas Vlachopoulos & Mark Diederichs

Authors
  1. Jeffrey Oke
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nicholas Vlachopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mark Diederichs
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jeffrey Oke.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-018-1418-0

Keywords

Search

Navigation