Skip to main content

Upper Bound Limit Analysis of Circular Tunnel in Cohesive-Frictional Soils Using the Node-Based Smoothed Finite Element Method

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Abstract

In this paper, a numerical procedure using the node-based smoothed finite element method (NS-FEM) is proposed to evaluate the stability of a plane strain circular tunnel in cohesive-frictional soils subjected to continuous loading on the ground surface. In the NS-FEM, the strain smoothing is calculated over smoothing domains associated with the nodes of the elements. The soil is described as a uniform Mohr–Coulomb material and it obeys an associated flow rule. The limit load and failure mechanisms of circular tunnel are calculated from solving the optimization problems. In this study, the influence of the soil weight (γD/c′), the ratio of tunnel diameter to its depth (H/D) on the stability numbers (σ s /c′) and collapse mechanisms are investigated. The results obtained from the present analysis are compared with the available literature for tunnels located below the horizontal ground surface.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Atkinson JH, Potts DM (1977) Stability of a shallow circular tunnel in cohesionless soils. Géotechnique 27(2):203–215

    Article  Google Scholar 

  2. Atkinson JH, Cairncross AM (1973) Collapse of a shallow tunnel in a Mohr–Coulomb material. In: Role of plasticity in soil mechanics, Cambridge

    Google Scholar 

  3. Cairncross AM (1973) Deformation around model tunnels in stiff clay. PhD thesis, University of Cambridge

    Google Scholar 

  4. Seneviratne HN (1979) Deformations and pore-pressures around model tunnels in soft clay. PhD thesis, University of Cambridge

    Google Scholar 

  5. Mair RJ (1979) Centrifugal modelling of tunnel construction in soft clay. PhD thesis, University of Cambridge

    Google Scholar 

  6. Chambon P, Corté JF (1994) Shallow tunnels in cohesionless soil: stability of tunnel face. J Geotech Eng 120(7):1148–1165

    Article  Google Scholar 

  7. Kirsch A (2010) Experimental investigation of the face stability of shallow tunnels in sand. Acta Geotech 5:43–62

    Article  Google Scholar 

  8. Idiger G, Aklik P, Wei W, Borja RI (2011) Centrifuge model test on the face stability of shallow tunnel. Acta Geotech 6:105–117

    Article  Google Scholar 

  9. Davis EH, Gunn MJ, Mair RJ, Seneviratne HN (1980) The stability of shallow tunnels and underground openings in cohesive material. Geotechnique 30(4):397–416

    Article  Google Scholar 

  10. Mühlhaus HB (1985) Lower bound solutions for circular tunnels in two and three dimensions. Rock Mech Rock Eng 18:37–52

    Article  Google Scholar 

  11. Leca E, Dormieux L (1990) Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material. Geotechnique 40(4):581–606

    Article  Google Scholar 

  12. Zhang C, Han K, Zhang D (2015) Face stability analysis of shallow circular tunnels in cohesive–frictional soils. Tunn Undergr Space Technol 50:345–357

    Article  Google Scholar 

  13. Sloan SW, Assadi A (1991) Undrained stability of a square tunnel in a soil whose strength increases linearly with depth. Comput Geotech 12(4):321–346

    Article  Google Scholar 

  14. Lyamin AV, Sloan SW (2000) Stability of a plane strain circular tunnel in a cohesive frictional soil. In: Proceedings of the J.R. Booker memorial symposium, Sydney, Australia, pp 139–153

    Google Scholar 

  15. Lyamin AV, Jack DL, Sloan SW (2001) Collapse analysis of square tunnels in cohesive-frictional soils. In: Proceedings of the first Asian-Pacific congress on computational mechanics, Sydney, Australia, pp 405–414

    Google Scholar 

  16. Yamamoto K, Lyamin AV, Wilson DW, Sloan SW, Abbo AJ (2011) Stability of a single tunnel in cohesive–frictional soil subjected to surcharge loading. Can Geotech J 48(12):1841–1854

    Article  Google Scholar 

  17. Yamamoto K, Lyamin AV, Wilson DW, Sloan SW, Abbo AJ (2011) Stability of a circular tunnel in cohesive–frictional soil subjected to surcharge loading. Comput Geotech 38(4):504–514

    Article  Google Scholar 

  18. Chen JS, Wu CT, Yoon S (2001) A stabilized conforming nodal integration for Galerkin meshfree method. Int J Numer Methods Eng 50:435–466

    Article  MATH  Google Scholar 

  19. Yoo JW, Moran B, Chen JS (2004) Stabilized conforming nodal integration in the natural-element method. Int J Numer Methods Eng 60:861–890

    Article  MATH  Google Scholar 

  20. Liu GR, Nguyen-Thoi T (2010) Smoothed finite element methods. CRC Press, New York

    Book  Google Scholar 

  21. Liu GR, Dai KY, Nguyen-Thoi T (2007) A smoothed finite element for mechanics problems. Comput Mech 39:859–877

    Article  MATH  Google Scholar 

  22. Liu GR, Nguyen-Thoi T, Nguyen-Xuan H, Lam KY (2009) A node based smoothed finite element method (NS-FEM) for upper bound solution to solid mechanics problems. Comput Struct 87:14–26

    Article  Google Scholar 

  23. Nguyen-Thoi T, Liu GR, Lam KY, Zhang GY (2009) A face-based smoothed finite element method (FS-FEM) for 3D linear and nonlinear solid mechanics problems using 4-node tetrahedral elements. Int J Numer Methods Eng 78:324–353

    Article  MATH  Google Scholar 

  24. Liu GR, Nguyen-Thoi T, Lam KY (2009) An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids. J Sound Vib 320:1100–1130

    Article  Google Scholar 

  25. Liu GR, Nguyen-Thoi T, Dai KY, Lam KY (2007) Theoretical aspects of the smoothed finite element method (SFEM). Int J Numer Methods Eng 71:902–930

    Article  MathSciNet  MATH  Google Scholar 

  26. Liu GR, Nguyen-Xuan H, Nguyen-Thoi T (2010) A theoretical study of S-FEM models: properties, accuracy and convergence rates. Int J Numer Methods Eng 84:1222–1256

    Article  MathSciNet  MATH  Google Scholar 

  27. Nguyen-Xuan H, Rabczuk T, Nguyen-Thoi T, Tran TN, Nguyen-Thanh N (2012) Computation of limit and shakedown loads using a node-based smoothed finite element method. Int J Numer Methods Eng 90:287–310

    Google Scholar 

  28. Le CV, Nguyen-Xuan H, Askes H, Bordas S, Rabczuk T, Nguyen-Vinh H (2010) A cell-based smoothed finite element method for kinematic limit analysis. Int J Numer Methods Eng 83:1651–1674

    Article  MathSciNet  MATH  Google Scholar 

  29. Nguyen-Xuan H, Liu GR (2015) An edge-based finite element method (ES-FEM) with adaptive scaled-bubble functions for plane strain limit analysis. Comput Methods Appl Mech Eng 285:877–905

    Article  MathSciNet  Google Scholar 

  30. Nguyen-Xuan H, Rabczuk T (2015) Adaptive selective ES-FEM limit analysis of cracked plane-strain structures. Frontiers Struct Civil Eng 9:478–490

    Article  Google Scholar 

  31. Nguyen-Xuan H, Wu CT, Liu GR (2016) An adaptive selective ES-FEM for plastic collapse analysis. Eur J Mech A/Solid. https://doi.org/10.1016/j.euromechsol.2016.02.005

  32. Nguyen-Thoi T, Rabczuk T, Lam-Phat T, Ho-Huu V, Phung-Van P (2014) Free vibration analysis of cracked Mindlin plate using an extended cell-based smoothed discrete shear gap method (XCS-DSG3). Theoret Appl Fract Mech 72:150–163

    Article  Google Scholar 

  33. Nguyen-Thoi T, Luong-Van H, Phung-Van P, Rabczuk T, Tran-Trung D (2013) Dynamic responses of composite plates on the Pasternak foundation subjected to a moving mass by a cell-based smoothed discrete shear gap (CS-FEM-DSG3) method. Int J Compos Mater 3(A):19–27

    Google Scholar 

  34. Nguyen-Thoi T, Phung-Van P, Nguyen-Thoi MH, Dang-Trung H (2015) An upper-bound limit analysis of Mindlin plates using CS-DSG3 method and second-order cone programming. J Comput Appl Math 281:32–48

    Article  MathSciNet  MATH  Google Scholar 

  35. Nguyen-Hoang S, Phung-Van P, Natarajan S, Kim H-G (2016) A combined scheme of edge-based and node-based smoothed finite element methods for Reissner-Mindlin flat shells. Eng Comput 32(2):267–284

    Article  Google Scholar 

  36. Nguyen-Thoi T, Phung-Van P, Nguyen-Hoang S, Lieu-Xuan Q (2014) A coupled alpha-FEM for dynamic analyses of 2D fluid–solid interaction problems. J Comput Appl Math 271:130–149

    Article  MathSciNet  MATH  Google Scholar 

  37. Wu SC, Liu GR, Zhang HO, Xu X, Li ZR (2009) A node-based smoothed point interpolation method (NS-PIM) for three-dimensional heat transfer problems. Int J Therm Sci 48:1367–1376

    Article  Google Scholar 

  38. Cui XY, Li ZC, Feng H, Feng SZ (2016) Steady and transient heat transfer analysis using a stable node-based smoothed finite element method. Int J Therm Sci 110:12–25

    Article  Google Scholar 

  39. Liu GR, Chen L, Nguyen-Thoi T, Zeng KY, Zhang GY (2010) A novel singular node-based smoothed finite element method (NS-FEM) for upper bound solutions of fracture problems. Int J Numer Methods Eng 83:1466–1497

    Article  MathSciNet  MATH  Google Scholar 

  40. Wang G, Cui XY, Liang ZM, Li GY (2015) A coupled smoothed finite element method (S-FEM) for structural-acoustic analysis of shells. Eng Anal Boundary Elem 61:207–217

    Article  MathSciNet  Google Scholar 

  41. Wang G, Cui XY, Feng H, Li GY (2015) A stable node-based smoothed finite element method for acoustic problems. Comput Methods Appl Mech Eng 297:348–370

    Article  MathSciNet  Google Scholar 

  42. Cui XY, Wang G, Li GY (2016) A nodal integration axisymmetric thin shell model using linear interpolation. Appl Math Model 40:2720–2742

    Article  MathSciNet  Google Scholar 

  43. Feng H, Cui XY, Li GY (2016) A stable nodal integration method with strain gradient for static and dynamic analysis of solid mechanics. Eng Anal Boundary Elem 62:78–92

    Article  MathSciNet  Google Scholar 

  44. Wang G, Cui XY, Li GY (2016) A rotation-free shell formulation using nodal integration for static and dynamic analyses of structures. Int J Numer Methods Eng 105:532–560

    Article  MathSciNet  Google Scholar 

  45. Wang G, Cui XY, Li GY (2015) Temporal stabilization nodal integration method for static and dynamic analyses of Reissner-Mindlin plates. Comput Struct 152:124–141

    Article  Google Scholar 

  46. Vo TM, Nguyen TM, Chau AN, Nguyen HC (2017) Stability of twin circular tunnels in cohesive-frictional soil using the node-based smoothed finite element method (NS-FEM). J VibroEng 19(1):520–538

    Article  Google Scholar 

  47. Vo TM, Chau AN, Nguyen TM, Nguyen HC. A node-based smoothed finite element method for stability analysis of dual square tunnels in cohesive-frictional soils. Scientia Iranica (in press)

    Google Scholar 

  48. Makrodimopoulos A, Martin CM (2006) Upper bound limit analysis using simplex strain elements and second-order cone programming. Int J Numer Anal Methods Geomech 31:835–865

    Article  MATH  Google Scholar 

  49. Mosek. The MOSEK optimization toolbox for MATLAB manual. http://www.mosek.com

  50. GiD 11.0.4. International Center for Numerical Methods in Engineering (CIMNE), Reference manual. http://www.cimne.com

  51. Chen WF (1975) Limit analysis and soil plasticity. Elsevier, Amsterdam

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to T. Nguyen-Minh or A. Chau-Ngoc .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Vo-Minh, T., Nguyen-Minh, T., Chau-Ngoc, A. (2018). Upper Bound Limit Analysis of Circular Tunnel in Cohesive-Frictional Soils Using the Node-Based Smoothed Finite Element Method. In: Nguyen-Xuan, H., Phung-Van, P., Rabczuk, T. (eds) Proceedings of the International Conference on Advances in Computational Mechanics 2017. ACOME 2017. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-10-7149-2_9

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-7149-2_9

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-7148-5

  • Online ISBN: 978-981-10-7149-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics