SpringerLink
Log in

Stress path analysis of advancing tunnel with supports installed close to face

  • Original Paper
  • Published:
Bulletin of Engineering Geology and the Environment Aims and scope Submit manuscript

Abstract

The post-peak response of elasto-plastic material is dependent upon the stress path it is subjected to. This paper analyses and compares the stress path and strain response of advancing tunnel, using two-dimension:1al plane strain (2D PS) and full three-dimensional step by step excavation and support (3D SBS) finite difference numerical model (FDM). Stress paths for 3D SBS model indicate higher stress relaxation and straining at unsupported spans as well as elastic recompression behind applied supports; these features are not evident in 2D PS models. Implications of these differences on tunnel response are discussed. The complex 3D stress evolution with tunnel construction is greatly simplified by considering major and minor principal stresses only, for the purpose of stress path generation. To verify that the formulation of stress path adopted here is sufficient to describe stress–strain evolution of 3D SBS tunnel model, a numerical simulation of “stress path following triaxial unloading test” is conducted using “simplified loading conditions.” Results show that the suggested test methodology has potential to map stress path of 3D SBS tunnel model for ideal geomaterial behavior. Also, improvement in measured strain response, as compared to 2D PS models, is observed.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (France)

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
Fig. 26
Fig. 27
Fig. 28
Fig. 29

Similar content being viewed by others

Abbreviations

\(d\) :

Tunnel diameter (m)

\(e\) :

Unsupported span (m)

\(u\) :

Radial displacement of tunnel walls (m)

\({\sigma }_{1}, {\sigma }_{2},{\sigma }_{3}\) :

Major, intermediate, and minor principal stress (MPa)

\({e}_{1}\),\({e}_{2}\), \({e}_{3}\) :

Major, intermediate, and minor principal strains

\({K}_{13}=\frac{{\sigma }_{1}}{{\sigma }_{3}}\) :

Stress ratio; ratio of major and minor principal stress

\({e}_{max}= \sqrt{{\left({e}_{xx}-{e}_{yy}\right)}^{2}+ {\left({e}_{yy}-{e}_{zz}\right)}^{2}+ {\left({e}_{zz}-{e}_{xx}\right)}^{2}+{{\tau }_{xy}}^{2}+{{\tau }_{yz}}^{2}+{{\tau }_{zx}}^{2}}\) :

= Maximum shear strain invariant.

\({e}_{vol}= {e}_{xx}+{e}_{yy}+{e}_{zz}\) :

Volumetric strain invariant

\({{e}_{max}}^{p}\) :

Plastic component of shear strain invariant

\({{e}_{vol}}^{p}\) :

Plastic component of volumetric strain invariant

References

  • Amberg F (2011) For a correct interpretation of ground reaction curves. Congr ISRM Bei**g China 12:16–21

    Google Scholar 

  • Barla M (2000) Stress paths around a circular tunnel. Riv Ital Di Geotec 34:53–58

    Google Scholar 

  • Barla M (1999) Tunnels in Swelling Ground–Simulation of 3D stress paths by triaxial laboratory testing. Ph. D. Thesis, Politecnico di Torino, Italy

  • Barla M (2008) Numerical simulation of the swelling behaviour around tunnels based on special triaxial tests. Tunn Undergr Sp Technol 23:508–521. https://doi.org/10.1016/j.tust.2007.09.002

    Article  Google Scholar 

  • Barla G, Debernardi D, Sterpi D (2012) Time-dependent modeling of tunnels in squeezing conditions. Int J Geomech 12(6):697–710

    Article  Google Scholar 

  • Beer G, Watson JO, Swoboda G (1987) Three-dimensional analysis of tunnels using infinite boundary elements. Comput Geotech 3:37–58. https://doi.org/10.1016/0266-352X(87)90031-0

    Article  Google Scholar 

  • Bellwald P (1990) A contribution to design of tunnels in Argillaceous rock. PhD. Thesis, Massachusetts Institute of Technology

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

    Article  Google Scholar 

  • Cai M (2008) Influence of stress path on tunnel excavation response - Numerical tool selection and modeling strategy. Tunn Undergr Sp Technol 23:618–628. https://doi.org/10.1016/j.tust.2007.11.005

    Article  Google Scholar 

  • Cai M et al (2007) Determination of residual strength parameters of jointed rock masses using the GSI system. Int J Rock Mech Min Sci 44(2):247–265

    Article  Google Scholar 

  • Cantieni L, Anagnostou G (2009a) The interaction between yielding supports and squeezing ground. Tunn Undergr Sp Technol 24:309–322. https://doi.org/10.1016/j.tust.2008.10.001

    Article  Google Scholar 

  • Cantieni L, Anagnostou G (2009b) The effect of the stress path on squeezing behavior in tunneling. Rock Mech Rock Eng 42:289–318. https://doi.org/10.1007/s00603-008-0018-9

    Article  Google Scholar 

  • Carranza-Torres C (2004) Elasto-plastic solution of tunnel problems using the generalized form of the hoek-brown failure criterion. International Journal of Rock Mechanics and Mining Sciences 41:629–639

    Article  Google Scholar 

  • Chen C-N, Huang W-Y (2007) Investigation of tunnel stress path during face advancement. J Mech 23:451–458

    Article  Google Scholar 

  • Chen CN, Chang WC (2017) Directional projection in stereographic representation of three-dimensional stress redistribution during tunnelling. Tunn Undergr Sp Technol 70:309–316. https://doi.org/10.1016/j.tust.2017.09.001

    Article  Google Scholar 

  • Chen HF, Sarip AF (2005) Elasticity and plasticity, 2005th edn. China Architecture and Building Press, pp. 95–167. , Bei**g (2005).

  • Chen X, Tang C, an, Yu J, et al (2018) Experimental investigation on deformation characteristics and permeability evolution of rock under confining pressure unloading conditions. J Cent South Univ 25:1987–2001. https://doi.org/10.1007/s11771-018-3889-2

    Article  Google Scholar 

  • Dai B, Zhao G, Dong L, Yang C (2015) Mechanical characteristics for rocks under different paths and unloading rates under confining pressures. Shock Vib 2015. https://doi.org/10.1155/2015/578748

  • De La Fuente M, Taherzadeh R, Sulem J et al (2019) Applicability of the convergence-confinement method to full-face excavation of circular tunnels with stiff support system. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-018-1694-8

    Article  Google Scholar 

  • Duddeck H (1991) Application of numerical analyses for tunnelling. Int J Numer Anal Methods Geomech 15:223–239. https://doi.org/10.1002/nag.1610150402

    Article  Google Scholar 

  • Eberhardt E (2001) Numerical modelling of three-dimension stress rotation ahead of tunnel face. Int J Rock Mech Min Sci 38:499–518

    Article  Google Scholar 

  • Galli G, Grimaldi A, Leonardi A (2004) Three-dimensional modelling of tunnel excavation and lining. Comput Geotech 31:171–183. https://doi.org/10.1016/j.compgeo.2004.02.003

    Article  Google Scholar 

  • Gioda G, Swoboda G (1999) Developments and applications of the numerical analysis of tunnels in continuous media. Int J Numer Anal Methods Geomech 23:1393–1405. https://doi.org/10.1002/(SICI)1096-9853(199911)23:13%3c1393::AID-NAG933%3e3.0.CO;2-Z

    Article  Google Scholar 

  • Hoek E, Carranza-Torres C, Corkum B (2002) Hoek-Brown failure criterion-2002 edition. Proceedings of NARMS-Tac 1(1):267–273

    Google Scholar 

  • Hoek E., Diederichs M.S. (2006) Empirical estimation of rock mass modulus. International Journal of Rock Mechanics and Mining Sciences 43:203–215

    Article  Google Scholar 

  • Itasca Consulting Group (2016) FLAC2D: Fast Lagrangian Analysis of Continua in 2 Dimensions. [Minneapolis, Minn.] : [Itasca Consulting Group], ©2016

  • Itasca Consulting Group (2002) FLAC3D: Fast Lagrangian Analysis of Continua in 3 Dimensions. [Minneapolis, Minn.] : [Itasca Consulting Group], ©2002.

  • Jaeger JC, Cook NGW, Zimmerman R (2009) Fundamentals of rock mechanics. John Wiley & Sons

    Google Scholar 

  • Jiang M, Sima J, Cui Y et al (2017) Experimental investigation of the deformation characteristics of natural loess under the stress paths in shield tunnel excavation. Int J Geomech 17:1–10. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000972

    Article  Google Scholar 

  • Kaiser PK, Yazici S, Maloney S (2001) Mining-induced stress change and consequences of stress path on excavation stability—a case study. Int J Rock Mech Min Sci 38:167–180. https://doi.org/10.1016/S1365-1609(00)00038-1

    Article  Google Scholar 

  • Kumasaka H (2007) Numerical computation of support characteristic curves for use in tunnel support design and their application to the characteristic curve method. Int J JCRM 3:1–6

    Google Scholar 

  • Lambe TW, Marr WA (1979) Stress path method. J Geotech Geoenvironmental Eng 105:

  • Martin CD, Kaiser PK, Christiansson R (2003) Stress, instability and design of underground excavations. Int J Rock Mech Min Sci 40:1027–1047. https://doi.org/10.1016/S1365-1609(03)00110-2

    Article  Google Scholar 

  • Ng CW, Lee GT (2005) Three-dimensional ground settlements and stress-transfer mechanisms due to open-face tunnelling. Can Geotech J 42:1015–1029. https://doi.org/10.1139/t05-025

    Article  Google Scholar 

  • Ng RMC, Lo KY (1985) The measurement of soil parameters relevant to tunnelling in clays. Can Geotech J 22:375–391. https://doi.org/10.1139/t86-056

    Article  Google Scholar 

  • Nguyen-Minh D, Guo C (1996) Recent progress in convergence confinement method. ISRM Int Symp - EUROCK 96:6

    Google Scholar 

  • Oke J, Vlachopoulos N, Diederichs M (2018) Improvement to the convergence-confinement method: inclusion of support installation proximity and stiffness. Rock Mech Rock Eng 51:1495–1519. https://doi.org/10.1007/s00603-018-1418-0

    Article  Google Scholar 

  • Pan XD, Hudson JA (1988) Plane strain analysis in modelling three-dimensional tunnel excavations. Int J ROCK Mech Min Geomech Abstr 25:

  • Panet M, Coyne AB, Bruno B, et al (2001a) Recommendations on the convergence-confinement method. AFTES 11

  • Panet M, GIVET PDC-O, GUILLOUX A, et al (2001b) The convergence–confinement method. Press ENPC

  • Schneider TR (1997) Behandlung der Störzonen beim Projekt des Gotthard Basistunnels. Felsbau 15(6):489–495

    Google Scholar 

  • Steiner W (1993) Swelling rock in tunnels: rock characterization, effect of horizontal stresses and construction procedures. Int J Rock Mech Min Sci 30:361–380

    Article  Google Scholar 

  • Sui ZL, Li ZG, Yang ZJ et al (2013) Tunnel strength and excavation effect under different stress paths. Appl Mech Mater 470:902–906. https://doi.org/10.4028/www.scientific.net/AMM.470.902

  • Vlachopoulos N, Diederichs MS (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 32:469–488. https://doi.org/10.1007/s10706-014-9727-x

    Article  Google Scholar 

  • Vogelhuber M, Anagnostou G, Kovári K (2004) The influence of pore water pressure on the mechanical behavior of squeezing rock. In: Proceedings of the 3rd Asian Rock Mechanics Symposium, Kyoto, Japan, November 2004

Download references

Author information

Authors and Affiliations

  1. Department of Mining Engineering, Visvesvaraya National Institute of Technology, South Ambazari Road, Nagpur, 440010, India

    Shashank Sharma, I. L. Muthreja & R. R. Yerpude

Authors
  1. Shashank Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. L. Muthreja
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. R. Yerpude
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shashank Sharma.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sharma, S., Muthreja, I.L. & Yerpude, R.R. Stress path analysis of advancing tunnel with supports installed close to face. Bull Eng Geol Environ 80, 6221–6244 (2021). https://doi.org/10.1007/s10064-021-02309-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10064-021-02309-z

Keywords

Search

Navigation