Skip to main content
SpringerLink
Log in

Global sensitivity analysis of certain and uncertain factors for a circular tunnel under seismic action

  • Research Article
  • Published:
Frontiers of Structural and Civil Engineering Aims and scope Submit manuscript

Abstract

There are many certain and uncertain design factors which have unrevealed rational effects on the generation of tensile damage and the stability of the circular tunnels during seismic actions. In this research paper, we have dedicated three certain and four uncertain design factors to quantify their rational effects using numerical simulations and the Sobol’s sensitivity indices. Main effects and interaction effects between the design factors have been determined supporting on variance-based global sensitivity analysis. The results detected that the concrete modulus of elasticity for the tunnel lining has the greatest effect on the tensile damage generation in the tunnel lining during the seismic action. In the other direction, the interactions between the concrete density and both of concrete modulus of elasticity and tunnel diameter have appreciable effects on the tensile damage. Furthermore, the tunnel diameter has the deciding effect on the stability of the tunnel structure. While the interaction between the tunnel diameter and concrete density has appreciable effect on the stability process. It is worthy to mention that Sobol’s sensitivity indices manifested strong efficiency in detecting the roles of each design factor in cooperation with the numerical simulations explaining the responses of the circular tunnel during seismic actions.

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

Similar content being viewed by others

References

  1. Akhlaghi T, Nikkar A. Effect of vertically propagating shear waves on seismic behavior of circular tunnels. Hindawi the Scientific World Journal, 2014, 2014, 1–10

    Google Scholar 

  2. Hashash Y M A, Hook J J, Schmidt B, I-Chiang Yao J. Seismic design and analysis of underground structure. Tunnelling and Underground Space Technology, 2001, 16(4): 247–293

    Google Scholar 

  3. Nariman N A, Hussain R R, Msekh M A, Karampour P. Prediction meta-models for the responses of a circular tunnel during earthquakes. Underground Space, 2019, 4(1): 31–47

    Google Scholar 

  4. Nariman N A, Ramazan A, Mohammad I I. Application of coupled XFEM-BCQO in the structural optimization of a circular tunnel lining subjected to a ground motion. Frontiers of Structural and Civil Engineering, 2019 (in press)

    Google Scholar 

  5. Mollon G, Dias D, Soubra A H. Probabilistic analysis and design of circular tunnels against face stability. International Journal of Geomechanics, 2009, 9(6): 237–249

    Google Scholar 

  6. Kalab Z, Stemon P. Influence of seismic events on shallow geotechnical structures. Acta Montanistica Slovaca, 2017, 22(4): 412–421

    Google Scholar 

  7. Ghasemi H, Park H S, Rabczuk T. A level-set based IGA formulation for topology optimization of flexoelectric materials. Computer Methods in Applied Mechanics and Engineering, 2017, 313: 239–258

    MathSciNet  Google Scholar 

  8. Ghasemi H, Brighenti R, Zhuang X, Muthu J, Rabczuk T. Optimum fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach. Structural and Multidisciplinary Optimization, 2015, 51(1): 99–112

    MathSciNet  Google Scholar 

  9. Zhang C, Nanthakumar S S, Lahmer T, Rabczuk T. Multiple cracks identification for piezoelectric structures. International Journal of Fracture, 2017, 206(2): 151–169

    Google Scholar 

  10. Nanthakumar S, Zhuang X, Park H, Rabczuk T. Topology optimization of flexoelectric structures. Journal of the Mechanics and Physics of Solids, 2017, 105: 217–234

    MathSciNet  Google Scholar 

  11. Nanthakumar S, Lahmer T, Zhuang X, Park H S, Rabczuk T. Topology optimization of piezoelectric nanostructures. Journal of the Mechanics and Physics of Solids, 2016, 94: 316–335

    MathSciNet  Google Scholar 

  12. Nanthakumar S, Lahmer T, Zhuang X, Zi G, Rabczuk T. Detection of material interfaces using a regularized level set method in piezoelectric structures. Inverse Problems in Science and Engineering, 2016, 24(1): 153–176

    MathSciNet  Google Scholar 

  13. Nanthakumar S, Valizadeh N, Park H, Rabczuk T. Surface effects on shape and topology optimization of nanostructures. Computational Mechanics, 2015, 56(1): 97–112

    MathSciNet  MATH  Google Scholar 

  14. Nanthakumar S S, Lahmer T, Rabczuk T. Detection of flaws in piezoelectric structures using extended FEM. International Journal for Numerical Methods in Engineering, 2013, 96(6): 373–389

    MathSciNet  MATH  Google Scholar 

  15. Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31

    Google Scholar 

  16. Vu-Bac N, Silani M, Lahmer T, Zhuang X, Rabczuk T. A unified framework for stochastic predictions of mechanical properties of polymeric nanocomposites. Computational Materials Science, 2015, 96: 520–535

    Google Scholar 

  17. Vu-Bac N, Rafiee R, Zhuang X, Lahmer T, Rabczuk T. Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters. Composites. Part B, Engineering, 2015, 68: 446–464

    Google Scholar 

  18. Rabczuk T, Akkermann J, Eibl J. A numerical model for reinforced concrete structures. International Journal of Solids and Structures, 2005, 42(5-6): 1327–1354

    MATH  Google Scholar 

  19. Bazant Z P. Why continuum damage is nonlocal: Micromechanics arguments. Journal of Engineering Mechanics, 1991, 117(5): 1070–1087

    Google Scholar 

  20. Thai T Q, Rabczuk T, Bazilevs Y, Meschke G. A higher-order stress-based gradient-enhanced damage model based on isogeo-metric analysis. Computer Methods in Applied Mechanics and Engineering, 2016, 304: 584–604

    MathSciNet  MATH  Google Scholar 

  21. Fleck N A, Hutchinson J W. A phenomenological theory for strain gradient effects in plasticity. Journal of the Mechanics and Physics of Solids, 1993, 41(12): 1825–1857

    MathSciNet  MATH  Google Scholar 

  22. Rabczuk T, Eibl J. Simulation of high velocity concrete fragmentation using SPH/MLSPH. International Journal for Numerical Methods in Engineering, 2003, 56(10): 1421–1444

    MATH  Google Scholar 

  23. Rabczuk T, Eibl J, Stempniewski L. Numerical analysis of high speed concrete fragmentation using a meshfree Lagrangian method. Engineering Fracture Mechanics, 2004, 71(4-6): 547–556

    Google Scholar 

  24. Rabczuk T, Xiao S P, Sauer M. Coupling of meshfree methods with nite elements: Basic concepts and test results. Communications in Numerical Methods in Engineering, 2006, 22(10): 1031–1065

    MathSciNet  MATH  Google Scholar 

  25. Rabczuk T, Eibl J. Modelling dynamic failure of concrete with meshfree methods. International Journal of Impact Engineering, 2006, 32(11): 1878–1897

    Google Scholar 

  26. Etse G, Willam K. Failure analysis of elastoviscoplastic material models. Journal of Engineering Mechanics, 1999, 125(1): 60–69

    Google Scholar 

  27. Miehe C, Hofacker M, Welschinger F. A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering, 2010, 199(45-48): 2765–2778

    MathSciNet  MATH  Google Scholar 

  28. Amiri F, Millan D, Arroyo M, Silani M, Rabczuk T. Fourth order phase-field model for local max-ent approximants applied to crack propagation. Computer Methods in Applied Mechanics and Engineering, 2016, 312(C): 254–275

    MathSciNet  Google Scholar 

  29. Areias P, Rabczuk T, Msekh M. Phase-field analysis of finite-strain plates and shells including element subdivision. Computer Methods in Applied Mechanics and Engineering, 2016, 312(C): 322–350

    MathSciNet  Google Scholar 

  30. Msekh M A, Silani M, Jamshidian M, Areias P, Zhuang X, Zi G, He P, Rabczuk T. Predictions of J integral and tensile strength of clay/epoxy nanocomposites material using phase-field model. Composites. Part B, Engineering, 2016, 93: 97–114

    Google Scholar 

  31. Hamdia K, Msekh M A, Silani M, Vu-Bac N, Zhuang X, Nguyen-Thoi T, Rabczuk T. Uncertainty quantication of the fracture properties of polymeric nanocomposites based on phase-field modeling. Composite Structures, 2015, 133: 1177–1190

    Google Scholar 

  32. Msekh M A, Sargado M, Jamshidian M, Areias P, Rabczuk T. ABAQUS implementation of phase-field model for brittle fracture. Computational Materials Science, 2015, 96: 472–484

    Google Scholar 

  33. Amiri F, Millán D, Shen Y, Rabczuk T, Arroyo M. Phase-field modeling of fracture in linear thin shells. Theoretical and Applied Fracture Mechanics, 2014, 69: 102–109

    Google Scholar 

  34. Hamdia K M, Zhuang X, He P, Rabczuk T. Fracture toughness of polymeric particle nanocomposites: Evaluation of Models performance using Bayesian method. Composites Science and Technology, 2016, 126: 122–129

    Google Scholar 

  35. Rabczuk T, Belytschko T, Xiao S P. Stable particle methods based on Lagrangian kernels. Computer Methods in Applied Mechanics and Engineering, 2004, 193(12-14): 1035–1063

    MathSciNet  MATH  Google Scholar 

  36. Rabczuk T, Belytschko T. Adaptivity for structured meshfree particle methods in 2D and 3D. International Journal for Numerical Methods in Engineering, 2005, 63(11): 1559–1582

    MathSciNet  MATH  Google Scholar 

  37. Nguyen V P, Rabczuk T, Bordas S, Duflot M. Meshless methods: A review and computer implementation aspects. Mathematics and Computers in Simulation, 2008, 79(3): 763–813

    MathSciNet  MATH  Google Scholar 

  38. Zhuang X, Cai Y, Augarde C. A meshless sub-region radial point interpolation method for accurate calculation of crack tip elds. Theoretical and Applied Fracture Mechanics, 2014, 69: 118–125

    Google Scholar 

  39. Zhuang X, Zhu H, Augarde C. An improved meshless Shepard and least square method possessing the delta property and requiring no singular weight function. Computational Mechanics, 2014, 53(2): 343–357

    MathSciNet  MATH  Google Scholar 

  40. Zhuang X, Augarde C, Mathisen K. Fracture modelling using meshless methods and level sets in 3D: Framework and modelling. International Journal for Numerical Methods in Engineering, 2012, 92(11): 969–998

    MathSciNet  MATH  Google Scholar 

  41. Chen L, Rabczuk T, Bordas S, Liu GR, Zeng KY, Kerfriden P. Extended finite element method with edge-based strain smoothing (Esm-XFEM) for linear elastic crack growth. Computer Methods in Applied Mechanics and Engineering, 2012, 209-212(4): 250–265

    MathSciNet  MATH  Google Scholar 

  42. Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 1999, 45(5): 601–620

    MATH  Google Scholar 

  43. Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 1999, 46(1): 131–150

    MathSciNet  MATH  Google Scholar 

  44. Vu-Bac N, Nguyen-Xuan H, Chen L, Lee C K, Zi G, Zhuang X, Liu G R, Rabczuk T. A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics. Journal of Applied Mathematics, 2013, 2013, 978026

    MathSciNet  MATH  Google Scholar 

  45. Bordas S P A, Natarajan S, Kerfriden P, Augarde C E, Mahapatra D R, Rabczuk T, Pont S D. On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/ GFEM/PUFEM). International Journal for Numerical Methods in Engineering, 2011, 86(4-5): 637–666

    MATH  Google Scholar 

  46. Bordas S P A, Rabczuk T, Hung N X, Nguyen V P, Natarajan S, Bog T, Quan D M, Hiep N V. Strain Smoothing in FEM and XFEM. Computers & Structures, 2010, 88(23-24): 1419–1443

    Google Scholar 

  47. Rabczuk T, Zi G, Gerstenberger A, Wall W A. A new crack tip element for the phantom node method with arbitrary cohesive cracks. International Journal for Numerical Methods in Engineering, 2008, 75(5): 577–599

    MATH  Google Scholar 

  48. Chau-Dinh T, Zi G, Lee P S, Rabczuk T, Song J H. Phantom-node method for shell models with arbitrary cracks. Computers & Structures, 2012, 92-93: 242–256

    Google Scholar 

  49. Song J H, Areias P M A, Belytschko T. A method for dynamic crack and shear band propagation with phantom nodes. International Journal for Numerical Methods in Engineering, 2006, 67(6): 868–893

    MATH  Google Scholar 

  50. Areias P M A, Song J H, Belytschko T. Analysis of fracture in thin shells by overlapping paired elements. Computer Methods in Applied Mechanics and Engineering, 2006, 195(41-43): 5343–5360

    MATH  Google Scholar 

  51. Rabczuk T, Areias P M A. A meshfree thin shell for arbitrary evolving cracks based on an external enrichment. CMES-Computer Modeling in Engineering and Sciences, 2006, 16(2): 115–130

    Google Scholar 

  52. Zi G, Rabczuk T, Wall W A. Extended meshfree methods without branch enrichment for cohesive cracks. Computational Mechanics, 2007, 40(2): 367–382

    MATH  Google Scholar 

  53. Rabczuk T, Bordas S, Zi G. A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics. Computational Mechanics, 2007, 40(3): 473–495

    MATH  Google Scholar 

  54. Rabczuk T, Zi G. A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics, 2007, 39(6): 743–760

    MATH  Google Scholar 

  55. Rabczuk T, Areias P M A, Belytschko T. A meshfree thin shell method for nonlinear dynamic fracture. International Journal for Numerical Methods in Engineering, 2007, 72(5): 524–548

    MathSciNet  MATH  Google Scholar 

  56. Bordas S, Rabczuk T, Zi G. Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment. Engineering Fracture Mechanics, 2008, 75(5): 943–960

    Google Scholar 

  57. Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A geometrically nonlinear three dimensional cohesive crack method for reinforced concrete structures. Engineering Fracture Mechanics, 2008, 75(16): 4740–4758

    Google Scholar 

  58. Rabczuk T, Gracie R, Song J H, Belytschko T. Immersed particle method for fluid-structure interaction. International Journal for Numerical Methods in Engineering, 2010, 81(1): 48–71

    MathSciNet  MATH  Google Scholar 

  59. Rabczuk T, Bordas S, Zi G. On three-dimensional modelling of crack growth using partition of unity methods. Computers & Structures, 2010, 88(23-24): 1391–1411

    Google Scholar 

  60. Amiri F, Anitescu C, Arroyo M, Bordas S, Rabczuk T. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics, 2014, 53(1): 45–57

    MathSciNet  MATH  Google Scholar 

  61. Talebi H, Samaniego C, Samaniego E, Rabczuk T. On the numerical stability and mass-lumping schemes for explicit enriched meshfree methods. International Journal for Numerical Methods in Engineering, 2012, 89(8): 1009–1027

    MathSciNet  MATH  Google Scholar 

  62. Nguyen-Thanh N, Zhou K, Zhuang X, Areias P, Nguyen-Xuan H, Bazilevs Y, Rabczuk T. Isogeometric analysis of large-deformation thin shells using RHTsplines for multiple-patch coupling. Computer Methods in Applied Mechanics and Engineering, 2017, 316: 1157–1178

    MathSciNet  Google Scholar 

  63. Nguyen-Thanh N, Valizadeh N, Nguyen M N, Nguyen-Xuan H, Zhuang X, Areias P, Zi G, Bazilevs Y, De Lorenzis L, Rabczuk T. An extended isogeometric thin shell analysis based on Kirchho-Love theory. Computer Methods in Applied Mechanics and Engineering, 2015, 284: 265–291

    MathSciNet  MATH  Google Scholar 

  64. Jia Y, Anitescu C, Ghorashi S, Rabczuk T. Extended isogeometric analysis for material interface problems. IMA Journal of Applied Mathematics, 2015, 80(3): 608–633

    MathSciNet  MATH  Google Scholar 

  65. Ghorashi S, Valizadeh N, Mohammadi S, Rabczuk T. T-spline based XIGA for fracture nalysis of orthotropic media. Computers & Structures, 2015, 147: 138–146

    Google Scholar 

  66. Rabczuk T, Belytschko T. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343

    MATH  Google Scholar 

  67. Rabczuk T, Areias P M A. A new approach for modelling slip lines in geological materials with cohesive models. International Journal for Numerical and Analytical Methods in Engineering, 2006, 30(11): 1159–1172

    MATH  Google Scholar 

  68. Rabczuk T, Belytschko T. Application of particle methods to static fracture of reinforced concrete structures. International Journal of Fracture, 2006, 137(1-4): 19–49

    MATH  Google Scholar 

  69. Rabczuk T, Belytschko T. A three dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29-30): 2777–2799

    MathSciNet  MATH  Google Scholar 

  70. Rabczuk T, Areias P M A, Belytschko T. A simplied meshfree method for shear bands with cohesive surfaces. International Journal for Numerical Methods in Engineering, 2007, 69(5): 993–1021

    MATH  Google Scholar 

  71. Rabczuk T, Samaniego E. Discontinuous modelling of shear bands using adaptive meshfree methods. Computer Methods in Applied Mechanics and Engineering, 2008, 197(6-8): 641–658

    MathSciNet  MATH  Google Scholar 

  72. Rabczuk T, Song J H, Belytschko T. Simulations of instability in dynamic fracture by the cracking particles method. Engineering Fracture Mechanics, 2009, 76(6): 730–741

    Google Scholar 

  73. Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37-40): 2437–2455

    MATH  Google Scholar 

  74. Cai Y, Zhuang X, Zhu H. A generalized and ecient method for nite cover generation in the numerical manifold method. International Journal of Computational Methods, 2013, 10(5): 1350028

    MathSciNet  MATH  Google Scholar 

  75. Liu G, Zhuang X, Cui Z. Three-dimensional slope stability analysis using independent cover based numerical manifold and vector method. Engineering Geology, 2017, 225: 83–95

    Google Scholar 

  76. Nguyen B H, Zhuang X, Wriggers P, Rabczuk T, Mear M E, Tran H D. Isogeometric symmetric Galerkin boundary element method for three-dimensional elasticity problems. Computer Methods in Applied Mechanics and Engineering, 2017, 323: 132–150

    MathSciNet  Google Scholar 

  77. Nguyen B H, Tran H D, Anitescu C, Zhuang X, Rabczuk T. An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems. Computer Methods in Applied Mechanics and Engineering, 2016, 306: 252–275

    MathSciNet  Google Scholar 

  78. Zhu H, Wu W, Chen J, Ma G, Liu X, Zhuang X. Integration of three dimensional discontinuous deformation analysis (DDA) with binocular photogrammetry for stability analysis of tunnels in blocky rock mass. Tunnelling and Underground Space Technology, 2016, 51: 30–40

    Google Scholar 

  79. Wu W, Zhu H, Zhuang X, Ma G, Cai Y. A multi-shell cover algorithm for contact detection in the three dimensional discontinuous deformation analysis. Theoretical and Applied Fracture Mechanics, 2014, 72: 136–149

    Google Scholar 

  80. Cai Y, Zhu H, Zhuang X. A continuous/discontinuous deformation analysis (CDDA) method based on deformable blocks for fracture modelling. Frontiers of Structural and Civil Engineering, 2013, 7(4): 369–378

    Google Scholar 

  81. Nguyen-Xuan H, Liu G R, Bordas S, Natarajan S, Rabczuk T. An adaptive singular ES-FEM for mechanics problems with singular eld of arbitrary order. Computer Methods in Applied Mechanics and Engineering, 2013, 253: 252–273

    MathSciNet  MATH  Google Scholar 

  82. Areias P, Rabczuk T. Steiner-point free edge cutting of tetrahedral meshes with applications in fracture. Finite Elements in Analysis and Design, 2017, 132: 27–41

    Google Scholar 

  83. Areias P, Reinoso J, Camanho P, Rabczuk T. A constitutive-based element-by-element crack propagation algorithm with local mesh refinement. Computational Mechanics, 2015, 56(2): 291–315

    MathSciNet  MATH  Google Scholar 

  84. Areias P M A, Rabczuk T, Camanho P P. Finite strain fracture of 2D problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics, 2014, 72: 50–63

    Google Scholar 

  85. Areias P, Rabczuk T, Dias-da-Costa D. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 2013, 110: 113–137

    Google Scholar 

  86. Areias P, Rabczuk T, Camanho P P. Initially rigid cohesive laws and fracture based on edge rotations. Computational Mechanics, 2013, 52(4): 931–947

    MATH  Google Scholar 

  87. Areias P, Rabczuk T. Finite strain fracture of plates and shells with congurational forces and edge rotation. International Journal for Numerical Methods in Engineering, 2013, 94(12): 1099–1122

    MathSciNet  MATH  Google Scholar 

  88. Silani M, Talebi H, Hamouda A S, Rabczuk T. Nonlocal damage modeling in clay/epoxy nanocomposites using a multiscale approach. Journal of Computational Science, 2016, 15: 18–23

    Google Scholar 

  89. Talebi H, Silani M, Rabczuk T. Concurrent multiscale modelling of three dimensional crack and dislocation propagation. Advances in Engineering Software, 2015, 80: 82–92

    Google Scholar 

  90. Silani M, Talebi H, Ziaei-Rad S, Hamouda A M S, Zi G, Rabczuk T. A three dimensional extended Arlequin method for dynamic fracture. Computational Materials Science, 2015, 96: 425–431

    Google Scholar 

  91. Silani M, Ziaei-Rad S, Talebi H, Rabczuk T. A semi-concurrent multiscale approach for modeling damage in nanocomposites. Theoretical and Applied Fracture Mechanics, 2014, 74: 30–38

    Google Scholar 

  92. Talebi H, Silani M, Bordas S, Kerfriden P, Rabczuk T. A computational library for multiscale modelling of material failure. Computational Mechanics, 2014, 53(5): 1047–1071

    MathSciNet  Google Scholar 

  93. Talebi H, Silani M, Bordas S P A, Kerfriden P, Rabczuk T. Molecular dynamics/XFEM coupling by a three-dimensional extended bridging domain with applications to dynamic brittle fracture. International Journal for Multiscale Computational Engineering, 2013, 11(6): 527–541

    Google Scholar 

  94. Yang S W, Budarapu P R, Mahapatra D R, Bordas S P A, Zi G, Rabczuk T. A meshless adaptive multiscale method for fracture. Computational Materials Science, 2015, 96: 382–395

    Google Scholar 

  95. Budarapu P, Gracie R, Bordas S, Rabczuk T. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics, 2014, 53(6): 1129–1148

    Google Scholar 

  96. Budarapu P R, Gracie R, Yang S W, Zhuang X, Rabczuk T. Ecient coarse graining in multiscale modeling of fracture. Theoretical and Applied Fracture Mechanics, 2014, 69: 126–143

    Google Scholar 

  97. Zhuang X, Wang Q, Zhu H. Multiscale modelling of hydro-mechanical couplings in quasi-brittle materials. International Journal of Fracture, 2017, 204(1): 1–27

    Google Scholar 

  98. Zhu H, Wang Q, Zhuang X. A nonlinear semi-concurrent multiscale method for fractures. International Journal of Impact Engineering, 2016, 87: 65–82

    Google Scholar 

  99. Zhuang X, Wang Q, Zhu H. A 3D computational homogenization model for porous material and parameters identification. Computational Materials Science, 2015, 96: 536–548

    Google Scholar 

  100. Kouznetsova V, Geers M G D, Brekelmans W A M. Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme. International Journal for Numerical Methods in Engineering, 2002, 54(8): 1235–1260

    MATH  Google Scholar 

  101. Rabczuk T, Ren H. A peridynamics formulation for quasi-static fracture and contact in rock. Engineering Geology, 2017, 225: 42–48

    Google Scholar 

  102. Amani J, Oterkus E, Areias P, Zi G, Nguyen-Thoi T, Rabczuk T. A non-ordinary state-based peridynamics formulation for thermoplastic fracture. International Journal of Impact Engineering, 2016, 87: 83–94

    Google Scholar 

  103. Ren H, Zhuang X, Rabczuk T. A new Peridynamic formulation with shear deformation for elastic solid. Journal of Micromecha-nics and Molecular Physics, 2016, 1(2): 1650009

    Google Scholar 

  104. Ren H, Zhuang X, Cai Y, Rabczuk T. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476

    MathSciNet  Google Scholar 

  105. Ren H, Zhuang X, Rabczuk T. Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782

    MathSciNet  Google Scholar 

  106. Glen G, Isaacs K. Estimating sobol sensitivity indices using correlations. Journal of Environmental Modelling and Software, 2012, 37: 157–166

    Google Scholar 

  107. Nossent J, Elsen P, Bauwens W. Sobol sensitivity analysis of a complex environmental model. Journal of Environmental Modelling and Software, 2011, 26(12): 1515–1525

    Google Scholar 

  108. Zhang X Y, Trame M N, Lesko L J, Schmidt S. Sobol sensitivity analysis: A tool to guide the development and evaluation of systems pharmacology models. CPT: Pharmacometrics & Systems Pharmacology, 2015, 4(2): 69–79

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Tishk International University Sulaimani, Sulaimaniya, 46001, Iraq

    Nazim Abdul Nariman & Ilham Ibrahim Mohammad

  2. Civil Engineering Department, College of Engineering, King Saud University, Riyadh, 11421, Saudi Arabia

    Raja Rizwan Hussain

  3. Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak, 38156-875, Iran

    Peyman Karampour

Authors
  1. Nazim Abdul Nariman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Raja Rizwan Hussain
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ilham Ibrahim Mohammad
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Peyman Karampour
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nazim Abdul Nariman.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nariman, N.A., Hussain, R.R., Mohammad, I.I. et al. Global sensitivity analysis of certain and uncertain factors for a circular tunnel under seismic action. Front. Struct. Civ. Eng. 13, 1289–1300 (2019). https://doi.org/10.1007/s11709-019-0548-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11709-019-0548-0

Keywords

Search

Navigation