Skip to main content
SpringerLink
Log in

Elasto-plastic analysis of circular tunnel in rock mass with confining stress-dependent strain-softening behavior considering intermediate principal stress

  • Original Paper
  • Published:
Arabian Journal of Geosciences Aims and scope Submit manuscript

Abstract

The conventional generalized Hoek–Brown failure criterion neglects the influence of intermediate principal stress, which should be considered for investigating the elastoplastic behavior of circular tunnel in rock mass. The generalized three-dimensional Hoek–Brown criterion inherits the advantages of generalized two-dimensional Hoek–Brown criterion, but also takes the intermediate principal stress into account, and is employed to be yield function in this paper. Besides, the variable critical plastic softening parameter (η*) is also introduced to investigate the elastoplastic behavior of circular tunnel excavation in rock mass. Then a new numerical procedure is proposed and verified based on GZZ failure criterion with variable η*. The radial displacement and radius of the plastic softening zone (Rp) were overestimated using the conventional Hoek–Brown failure criterions. The effect of support pressure (Pi) was underestimated at lower level on elastoplastic behavior of poor-quality rock mass compared with GZZ failure criterion with variable η*. Finally, a series of parametric studies was executed by the proposed numerical procedure about the influences of initial stress, uniaxial compression strength and GSI on Rp, and plastic softening parameter (η) and η*.

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

Similar content being viewed by others

Abbreviations

\({\sigma }_{r}\) :

radial stress, MPa

\({\sigma }_{\theta }\) :

tangent stress, MPa

\({\sigma }_{z}\) :

axial stress, MPa

\({\sigma }_{0}\) :

initial stress, MPa

\({\sigma }_{c}\) :

uniaxial compression strength, MPa

\({\tau }_{oct}\) :

octahedral shear stress, MPa

\({\sigma }_{m,2}\) :

average stress of max and min principal stress, MPa

\({\varepsilon }_{\theta }\) :

tangent strain

\({\varepsilon }_{r}\) :

radial strain

\(\eta\) :

plastic softening parameter

\({\eta }^{*}\) :

critical plastic softening parameter

a, m b, s :

strength parameters of Hoek–Brown rock mass

\(E\) :

Young’s modulus, GPa

\(\nu\) :

Poisson’s ratio

\(G\) :

shear modulus, GPa

\({P}_{i}\) :

support pressure, MPa

\({R}_{0}\) :

tunnel radius, m

\({R}_{p}\) :

plastic zone radius, m

\(u\) :

radial displacement, mm

\(r\) :

radial distance from any point to the center of the circular tunnel, m

\(\psi\) :

dilation angle, °

\(M\) :

drop modulus in post peak stage, GPa

\({K}_{\psi }\) :

dilatancy coefficient of surrounding rock

\(\rho\) :

ratio between outer and inner radii of each annulus

References

  • Alonso E, Alejano LR, Varas F, Fdez-Manin G, Carranza-Torres C (2003) Ground response curves for rock masses exhibiting strain-softening behaviour. Int J Numer Anal Meth Geomech 27:1153–1185

    Article  Google Scholar 

  • Alejano LR, Alonso E (2005) Considerations of the dilatancy angle in rocks and rock masses. Int J Rock Mech Min Sci 42:481–507

    Article  Google Scholar 

  • Alonso E, Alejano LR, Fdez-Main G, Garcia-Bastante F (2008) Influence of postpeak properties in the application of the convergence-confinement for designing underground excavations. In: Proceedings of the 5th International Conference and Exhibition on Massive Mining Technology, Lulea, Sweden 793–802

  • Alejano LR, Alonso E, Rodriguez-Dono A, Fernandez-Manin G (2010) Application of the convergence-confinement method to tunnels in rock masses exhibiting Hoek-Brown strain-softening behaviour. Int J Rock Mech Min Sci 47:150–160

    Article  Google Scholar 

  • Alejano LR, Rodriguez-Dono A, Veiga M (2012) Plastic radii and longitudinal deformation profiles of tunnels excavated in strain-softening rock masses. Tunn Undergr Space Technol 30:169–182

    Article  Google Scholar 

  • Carranza-torres C, Fairhurst C (1999) The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion. Int J Rock Mech Min Sci 36(6):777–809

    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. Tunn Undergr Space Technol 15(2):187–213

    Article  Google Scholar 

  • Colmenares LB, Zoback MD (2002) A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks. Int J Rock Mech Min Sci 39(6):695–729

    Article  Google Scholar 

  • Cui L, Zheng JJ, Zhang RJ, Dong YK (2015) Elasto-plastic analysis of a circular opening in rock mass with confining stress-dependent strain-softening behavior. Tunn Undergr Space Technol 50:94–108

    Article  Google Scholar 

  • Dai Z, You T, Xu X, Zhu Q (2018) Removal of singularities in Hoek-Brown criterion and its numerical implementation and applications. Int J Geomech 18(10):04018127

    Article  Google Scholar 

  • Detournay E (1986) Elasto-plastic model of a deep tunnel for a rock with variable dilatancy. Rock Mech Rock Eng 19:99–108

    Article  Google Scholar 

  • Fenner R (1938) Untersuchungen Zur Erkenntnis Des Gebirgsdruckes Gluckauf 74(681–695):705–715

    Google Scholar 

  • Guan Z, Jiang Y, Tanabasi G (2007) Ground reaction analyses in conventional tunneling excavation. Tunn Undergr Space Technol 22:230–237

    Article  Google Scholar 

  • Guan K, Zhu W, Wei J, Liu X, Niu L, Wang X (2018) A finite strain numerical procedure for a circular tunnel in strain-softening rock mass with large deformation. Int J Rock Mech Min Sci 112:266–280

    Article  Google Scholar 

  • Haimson BC, Chang C (2000) A true triaxial cell for testing mechanical properties of rock, and its use to determine rock strength and deformability of Westerly granite. Int J Rock Mech Min Sci 37(1–2):285–296

    Article  Google Scholar 

  • Hoek E, Brown ET (1980) Empirical strength criterion of rock masses. J Geotech Geoenviron Eng ASCE 106(9):1013–1035

    Google Scholar 

  • Hoek E, Carranza-Torres CT, Corkum B (2002) Hoek-Brown failure criterion-2002 edition. In: Proceedings of the 5th North American Rock Mechanics Symposium and 17th Tunnelling Association of Canada Conference, Toronto 267–273

  • Jaeger JC, Cook NGW (1978) Fundamentals of rock mechanics. Chapman and Hall, London

    Google Scholar 

  • Kastner H (1949) Uber den Echten Gebiergsdruck beim bau Tiefliengender. Tunnel, 10. Vienna: Osterreich Bauzeitschrift

  • Lee YK, Pietruszczak S (2008) A new numerical procedure for elasto-plastic analysis of a circular opening excavated in a strain-softening rock mass. Tunn Undergr Space Technol 23(5):588–599

    Article  Google Scholar 

  • Lee YK, Pietruszczak S, Choi B (2012) Failure criteria for rocks based on smooth approximations to Mohr-Coulomb and Hoek–brown failure functions. Int J Rock Mech Min 56:146–160

    Article  Google Scholar 

  • Medhurst TP (1996) Estimation of the in situ strength and deformability of coal for engineering design. Ph.D. Thesis. University of Queensland, Australia

  • Obert L, Duvall WI (1967) Rock mechanics and the design of structure in rock. John Wiley and Sons, New York

    Google Scholar 

  • Ogawa T, Lo KY (1987) Effects of dilatancy and yield criteria on displacements around tunnels. Can Geotech J 24(1):100–113. https://doi.org/10.1139/t87-009

  • Pan XD, Hudson JA (1988) A simplified three-dimensional Hoek-Brown yield criterion. International Society for Rock Mechanics, ISRM International Symposium

    Google Scholar 

  • Park KH, Kim YJ (2006) Analytical solution for a circular opening in an elastic- brittle-plastic rock. Int J Rock Mech Min Sci 43(4):616–622

    Article  Google Scholar 

  • Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in Fortran. Cambridge University Press

    Google Scholar 

  • Priest SD (2005) Determination of shear strength and three-dimensional yield strength for the Hoek-Brown criterion. Rock Mech Rock Eng 38:299–327

    Article  Google Scholar 

  • Serrano A, Olalla C, Reig I (2011) Convergence of circular tunnels in elastoplastic rock masses with non-linear failure criteria and non-associated flow laws. Int J Rock Mech Min Sci 48:878–887

    Article  Google Scholar 

  • Sharan SK (2003) Elastic–brittle–plastic analysis of circular opening in Hoek-Brown media. Int J Rock Mech Min Sci 40:817–824

    Article  Google Scholar 

  • Sharan SK (2005) Exact and approximate solutions for displacements around circular openings in elasto-brittle-plastic Hoek-Brown rock. Int J Rock Mech Min Sci 42:542–549

    Article  Google Scholar 

  • Sharan SK (2008) Analytical solutions for stresses and displacements around a circular opening in a generalized Hoek-Brown rock. Int J Rock Mech Sci Geom Abstr 45:78–85

    Article  Google Scholar 

  • Wang SL, Yin XT, Tang H, Ge XR (2010) A new approach for analyzing circular tunnel in strain-softening rock masses. Int J Rock Mech Min Sci 47:170–178

    Article  Google Scholar 

  • Wang SL, Zheng H, Li CG, Ge XR (2011) A finite element implementation of strain-softening rock mass. Int J Rock Mech Min Sci 48:67–76

    Article  Google Scholar 

  • Xu S, Yu M (2006) The effect of the intermediate principal stress on the ground response of circular openings in rock mass. Rock Mech Rock Eng 39(2):169–181

    Article  Google Scholar 

  • Yu MH (2002) Advance in strength theories of materials under the complex stress state in the 20th century. Appl Mech Rev 55(3):169–218

    Article  Google Scholar 

  • Yu MH (2004) Unified strength theory and its applications. Springer, Berlin

    Book  Google Scholar 

  • Zhang L, Zhu HH (2007) Three-dimensional Hoek-Brown strength criterion for rocks. J Geotech Geoenviron Eng 133(9):1128–1135

    Article  Google Scholar 

  • Zhang C, Zhang Q, Zhao J, et al. (2010) Unified analytical solutions for a circular opening based on non-linear unified failure criterion. J Zhejiang Univ-Sci A (Appl Phys & Eng) 11(2):71–79

  • Zhang Q, Zhang C, Jiang B, Li N, Wang Y (2017) Elastoplastic coupling solution of circular openings in strain-softening rock mass considering pressure-dependent effect. Int J Geomech 18(1):04017132

    Article  Google Scholar 

  • Zhang Q, Zhu HH, Zhang L (2013) Modification of a generalized three-dimensional Hoek-Brown strength criterion. Int J Rock Mech Min 59:80–96

    Article  Google Scholar 

  • Zhang L (2008) A generalized three-dimensional Hoek-Brown strength criterion. Rock Mech Rock Eng 41(6):893–915

    Article  Google Scholar 

  • Zhou XP, Yang HQ, Zhang YX et al (2009) The effect of the intermediate principal stress on the ultimate bearing capacity of a foundation on rock masses. Comput Geotech 36:861–870

    Article  Google Scholar 

  • Zou J, Su Y (2016) Theoretical solutions of a circular tunnel with the influence of the out-of-plane stress based on the generalized Hoek-Brown failure criterion. Int J Geomech 16(3):06015006

    Article  Google Scholar 

Download references

Funding

This research was funded by the Shanghai Municipal Science and Technology Project (18DZ1201301; 19DZ1200900); Xiamen Road and Bridge Group (XM2017-TZ0151; XM2017-TZ0117); the project of Key Laboratory of Impact and Safety Engineering (Ningbo University), Ministry of Education (CJ202101); Shanghai Municipal Science and Technology Major Project (2021SHZDZX0100) and the Fundamental Research Funds for the Central Universities; Key Laboratory of Land Subsidence Monitoring and Prevention, Ministry of Natural Resources of the People's Republic of China (No. KLLSMP202101).

Author information

Authors and Affiliations

  1. School of Civil Engineering and Architecture, Zhejiang University of Science and Technology, Hangzhou, 310023, China

    Yansheng Deng & Baoping Zou

  2. College of Civil Engineering, Tongji University, Shanghai, 200092, China

    Yansheng Deng, Jianxiu Wang & Mingjing Jiang

  3. Key Laboratory of Karst Collapse Prevention, CAGS, Guilin, 541004, China

    Jianxiu Wang

  4. State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology), Chengdu, 610059, China

    Jianxiu Wang

  5. College of River and Ocean Engineering, Chongqing Jiaotong University, Chongqing, 400041, China

    Mingjing Jiang

Authors
  1. Yansheng Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianxiu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mingjing Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Baoping Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianxiu Wang.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Responsible Editor: Zeynal Abiddin Erguler

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deng, Y., Wang, J., Jiang, M. et al. Elasto-plastic analysis of circular tunnel in rock mass with confining stress-dependent strain-softening behavior considering intermediate principal stress. Arab J Geosci 14, 2191 (2021). https://doi.org/10.1007/s12517-021-08582-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12517-021-08582-2

Keywords

Search

Navigation