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Reinforcement Analysis Using the Finite Element Method

  • Sheng-hong ChenEmail author
Chapter
Part of the Springer Tracts in Civil Engineering book series (SPRTRCIENG)

Abstract

Earth anchors inclusive solid bars (bolt, rebar) and stranded wire cables, have been extensively exercised in a wide range of geotechnical engineering. Shotcrete is also prevalent for the purpose to restrain rock exposures from excessive deforming and loosening. The relationships of meso-structure property are at the heart of the FEM towards the performance of reinforced hydraulic structures. Based on experimental studies, this chapter presents comprehensive studies inclusive explicit (distinct) approach and implicit (equivalent) approach of reinforcement components and joints. Either of them exhibits intrinsic advantages and disadvantages. The former uses special elements to individually discretize joints and reinforcement components to extract detailed behaviors of reinforced structures, whereas the latter elaborates an equivalent constitutive relation neglecting the exact positions of joints and reinforcement components to provide the overall structural response. One of the major advancements achieved in this chapter is that the localized shear deformation at the intersection points of bolts/shotcrete layers with joints is taken into account, which enables to describe the behaviors of bolt/shotcrete at the joint in much more detail even with implicit approach. The other important advancement is the consideration of the interface between equivalent bolt-grout material and host rock, which makes it possible to simulate the pull-out mechanism of bolt with explicit approach. In addition to a number of validation examples interspersed within the context, this chapter is closed with three engineering application cases (underground cavern, cut slope, dam foundation).

References

  1. Aydan O. The stabilisation of rock engineering structures by rockbolts. Ph.D. thesis, Nagoya University, Japan; 1989.Google Scholar
  2. Aydan O, Kyoya T, Ichikawa Y, Kawamoto T. Anchorage performance and reinforcement effects of fully grouted rockbolts on rock excavations. In: Proceedings of the 6th ISRM congress (vol. 2). Montreal: ISRM; 1987. p. 757–60.Google Scholar
  3. Aydan O, Sezaki M, Kawamoto T. Mechanical and numerical modelling of shotcrete. In: Pande GN, Pietruszcak S, editors. NUMOG IV—international symposium on numerical models in geomechanics. Rotterdam: AA Balkema; 1992. p. 757–64.Google Scholar
  4. Azuar JJ. Stabilisation de massifs rocheux fissures par barres d’acier scellees. Rapport de recherche No. 73. Paris: Laboratoire Central des Ponts et Chaussees; 1977.Google Scholar
  5. Barley AD. Properties of anchor grout in a confined state. In: Littlejohn GS, editor. Ground anchorages and anchored structures—Proceedings of the international conference on institution of civil engineers (ICE). London: Thomas Telford; 1997a. p. 13–22.Google Scholar
  6. Barley AD. The single bore multiple anchor system. In: Littlejohn GS, editor. Ground anchorages and anchored structures—Proceedings of the international conference on institution of civil engineers (ICE). London: Thomas Telford; 1997b. p. 67–75.Google Scholar
  7. Bawden WF, Hyett AJ, Lausch P. An experimental procedure for the in situ testing of cable bolts. Int J Rock Mech Min Sci Geomech Abstr. 1992;29(5):525–33.CrossRefGoogle Scholar
  8. Beer G. An isoparametric joint/interface element for finite element analysis. Int J Numer Methods Eng. 1985;21(4):585–600.CrossRefGoogle Scholar
  9. Benmokrane B, Chekired M, Xu H. Monitoring behavior of grouted anchors using vibrating-wire gauges. J Geotech Eng ASCE. 1995a;121(6):466–75.CrossRefGoogle Scholar
  10. Benmokrane B, Chennouf A, Mitri HS. Laboratory evaluation of cement based grouts and grouted rock anchors. Int J Rock Mech Min Sci Geomech Abstr. 1995b;32(7):633–42.CrossRefGoogle Scholar
  11. Bickel JO, Kuesel TR, King EH. Tunnel engineering handbook. 2nd ed. New York: Chapman & Hall; 1996.Google Scholar
  12. Bjurstrom S. Shear strength of hard rock jointed reinforced by grouted untensioned bolts. In: Proceedings of the 3rd ISRM congress (vol. 2). Washington: National Academy of Science; 1974. p. 1194–9. Google Scholar
  13. Briaud JL, Powers WF, Weatherby DE. Should grouted anchors have short tendon bond length? J Geotech Geoenviron Eng ASCE. 1998;124(2):110–9.CrossRefGoogle Scholar
  14. Chen SH. Hydraulic structures. Berlin: Springer; 2015.CrossRefGoogle Scholar
  15. Chen SH, Egger P. Elasto-viscoplastic distinct modelling of bolt in jointed rock masses. In: Yuan JX, editor. Proceedings of the computer methods and advance in geomechanics. Wuhan, Rotterdam: AA Balkema; 1997. p. 1985–90.Google Scholar
  16. Chen SH, Egger P. Three dimensional elasto-viscoplastic finite element analysis of reinforced rock masses and its application. Int J Numer Anal Methods Geomech. 1999;23(1):61–78.CrossRefGoogle Scholar
  17. Chen SH, Pande GN. Rheological model and finite element analysis of jointed rock masses reinforced by passive, fully-grouted bolts. Int J Rock Mech Min Sci Geomech Abstr. 1994;31(3):273–7.CrossRefGoogle Scholar
  18. Chen SH, Fu CH, Shahrour I. Finite element analysis of jointed rock masses reinforced by fully-grouted bolts and shotcrete lining. Int J Rock Mech Min Sci. 2009;46(1):19–30.CrossRefGoogle Scholar
  19. Chen SH, Zhang X, Shahrour I. Composite element model for the bonded anchorage head of stranded wire cable in tension. Int J Numer Anal Methods Geomech. 2015;39(12):1352–68.CrossRefGoogle Scholar
  20. Desai CS, Zaman MM, Lightner JG, Siriwardane HJ. Thin-layer element for interfaces and joints. Int J Numer Anal Methods Geomech. 1984;8(1):19–43.CrossRefGoogle Scholar
  21. Desai CS, Muqtadir A, Scheele F. Interaction analysis of anchor-soil systems. J Geotech Eng ASCE. 1986;112(5):537–53.CrossRefGoogle Scholar
  22. Egger P. Ground improvement by passive rock bolts, experimental and theoretical studies, example. Memorie GEAM. 1992;29(1):5–10.Google Scholar
  23. Egger P, Fernandes H. Nouvelle presse triaxiale-etude de modeles discontinus boulonnes. In: Proceedings of the 5th ISRM congress (vol. 1, Theme A). Melbourne: Brown Prior Anderson Pty Ltd.; 1983. p. A171–5.Google Scholar
  24. Egger P, Pellet F. Strength and deformation properties of reinforced jointed media under true triaxial conditions. In: Wittke W, editor. Proceedings of the 7th ISRM congress. Rotterdam: AA Balkema; 1991. p. 215–20.Google Scholar
  25. Egger P, Zabuski L. Behaviour of rough bolted joints in direct shear tests. In: Wittke W, editor. Proceedings of the 7th ISRM congress. Rotterdam: AA Balkema; 1991. p. 1285–8.Google Scholar
  26. Fuller PG, Cox RHT. Mechanics of load transfer from steel tendons to cement based grout. In: Grundy P, Stevens LK, editors. Proceedings of the 5th Australian conference on the mechanics of structures and materials. Melbourne: Melbourne and Monash Universities; 1975. p. 189–203.Google Scholar
  27. Ghaboussi J, Wilson EL, Isenberg J. Finite element for rock joint interfaces. J Soil Mech Found Div ASCE. 1973;99(SM10):833–48.Google Scholar
  28. Goodman RE, Taylor RL, Brekke TL. A model for the mechanics of jointed rock. J Soil Mech Found Div ASCE. 1968;94(SM3):637–59.Google Scholar
  29. Goris JM, Conway JP. Grouted flexible tendons and scaling investigation. In: Proceedings of the 13th world mining congress. Rotterdam: AA Balkema; 1987. p. 783–92.Google Scholar
  30. Grasselli G. 3D behaviour of bolted rock joints: experimental and numerical study. Int J Rock Mech Min Sci. 2005;42(1):13–24.CrossRefGoogle Scholar
  31. Griffiths DV. Numerical modeling of interfaces using conventional finite element. In: Kawamoto T, Ichikawa Y, editors. Proceedings of the 4th international conference on numerical methods in geomechanics. Rotterdam: AA Balkema; 1985. p. 837–44.Google Scholar
  32. Hagenhofer F. NATM for tunnels with high overburden. Tunnels Tunn. 1990;22(5):51–2.Google Scholar
  33. Hassani FP, Rajaie H. An investigation into the optimization of a shotcrete cable bolt support systems. In: Proceedings of the 14th congress of the Council of Mining and Metallurgical Institution. London: IMM; 1990. p. 119–29.Google Scholar
  34. Hassani FP, Mitri HS, Khan UH, Rajaie H. Experimental and numerical studies of cable bolt support systems. In: Kaiser PK, McCreath DR, editors. Proceedings of the international symposium on rock supports in mining and underground construction. Rotterdam: AA Balkema; 1992. p. 411–7.Google Scholar
  35. Haykin S. Neural networks: a comprehensive foundation. New Jersey: Prentice Hall; 1999.zbMATHGoogle Scholar
  36. Hermann LR. Finite element analysis of contact problems. J Soil Mech Found Div ASCE. 1978;104(EM5):1043–57.Google Scholar
  37. Hoek E, Bray JW. Rock slope engineering. 3rd edition. London: Institute of Mining and Metallurgy; 1981.Google Scholar
  38. Hyett AJ, Bawden WF, Reichert RD. The effect of rock mass confinement and the bond strength of fully grouted cable bolts. Int J Rock Mech Min Sci Geomech Abstr. 1992;29(5):503–24.CrossRefGoogle Scholar
  39. Hyett AJ, Bawden WF, Macsporran GR, Moosavi M. A constitutive law for bond failure of fully grouted cable bolts using a modified Hoek cell. Int J Rock Mech Min Sci Geomech Abstr. 1995;32(1):12–36.CrossRefGoogle Scholar
  40. Jalalifar H, Aziz N. Analytical behaviour of bolt-joint intersection under lateral loading conditions. Rock Mech Rock Eng. 2010a;43(1):89–94.CrossRefGoogle Scholar
  41. Jalalifar H, Aziz N. Experimental and 3D numerical simulation of reinforced shear joints. Rock Mech Rock Eng. 2010b;43(1):95–103.CrossRefGoogle Scholar
  42. Jarrel DJ, Haberfield CM. Tendon/Grout interface performance in grouted anchors. In: Proceedings of the conference on ground anchorages and anchored structures. London: Institution of Civil Engineers (ICE); 1997.Google Scholar
  43. Kaiser PK, Yazici S, Nose J. Effect of stress change on the bond strength of fully grouted cables. Int Rock Mech Min Sci Geomech Abstr. 1992;29(3):293–306.CrossRefGoogle Scholar
  44. Kim NK. Performance of tension and compression anchors in weathered soil. J Geotech Geoenviron Eng ASCE. 2003;129(12):1138–50.CrossRefGoogle Scholar
  45. Kim NK, Park JS, Kim SK. Numerical simulation of ground anchors. Comput Geotech. 2007;34(6):498–507.CrossRefGoogle Scholar
  46. Kovári K. Erroneous concepts behind the new Austrian tunnelling method. Tunnels Tunn. 1994;26(11):38–42.Google Scholar
  47. Kropik C, Mang HA. Computational mechanics of the excavation of tunnels. Eng Comput. 1996;13(7):49–69.CrossRefGoogle Scholar
  48. Larsson H, Olofsson T. Bolt action in jointed rock. In: Proceedings of the international symposium on rock bolting. Rotterdam: AA Balkema; 1983. p. 33–46.Google Scholar
  49. Larsson H, Olofsson T, Stephansson O. Reinforcement of jointed rock mass—a non linear continuum approach. In: Proceedings of the international symposium on fundamentals of rock joints. Bjorkliden: Centek Publishers; 1985. p. 567–77.Google Scholar
  50. Lo KY, Ogawa T, Lukajic B, Dupak DD. Measurement of strength parameters of concrete-rock contact at the dam-foundation interface. Geotech Test J. 1991;14(4):383–94.CrossRefGoogle Scholar
  51. Mahtab M, Goodman RE. Three dimensional analysis of joint rock slope. In: Proceedings of the 2nd ISRM congress (vol. 3). Beograd: Privredni Pregled; 1970. p. 353–60.Google Scholar
  52. Marence M, Swoboda G. Numerical model for rock bolts with consideration of rock joint movements. Rock Mech Rock Eng. 1995;28(3):145–65.CrossRefGoogle Scholar
  53. Ministry of Construction of the People’s Republic of China. (GB/T50266-99) Standard for tests method of engineering rock masses. Beijing: Research Institute of standards and norms (MOC); 1999 (in Chinese).Google Scholar
  54. Mitri HS, Edrissi R, Henning J. Finite element modelling of cable-bolted slopes in hard rock underground mines. In: Proceedings of the SME annual meeting. Alburquerque: SME; 1993. p. 94–116.Google Scholar
  55. Mitri HS, Rajaie H. Stress analysis of rock mass with cable support—a finite element approach. In: Proceedings of the conference on stresses in underground structures. Ontario: CANMET; 1990. p. 110–9.Google Scholar
  56. Müller L. Removing the misconceptions on the new Austrian tunnelling method. Tunnels Tunn. 1990;22(special issue):15–18.Google Scholar
  57. Ng CWW, Lee KM, Tang DKW. Three-dimensional numerical investigations of new Austrian tunneling method (NATM) twin tunnel interactions. Can Geotech J. 2004;41(3):523–39.CrossRefGoogle Scholar
  58. Pande GN, Gerrard CM. The behaviour of reinforced jointed rock masses under various simple loading states. In: Proceedings of the 5th ISRM congress. Melbourne: Brown Prior Anderson Pty Ltd. 1983;F217–23.Google Scholar
  59. Pande GN, Beer G, Williams JR. Numerical methods in rock mechanics. New York: Wiley; 1990.zbMATHGoogle Scholar
  60. Pietro T. Carl Akeley—a tribute to the founder of Shotcrete. Shotcrete. 2002, summer:10–12.Google Scholar
  61. Pietruszczak ST, Mróz Z. Finite element analysis of deformation of strain softening materials. Int J Numer Methods Eng. 1981;17(3):327–34.CrossRefGoogle Scholar
  62. Qiang S, Chen SH. A new three-dimensional element model of rock bolt. Chin J Rock Mechan Eng. 2001;20(supp 2):1476–82 (in Chinese).Google Scholar
  63. Rabcewicz L. The new Austrian tunnelling method (part two). Water Power. 1964;16(12):511–5.Google Scholar
  64. Rabcewicz L. The new Austrian tunnelling method (part three). Water Power. 1965;17(1):19–24.Google Scholar
  65. Rokahr RB, Stark A, Zachow R. On the art of interpreting measurement results. Felsbau. 2002;20(2):16–21.Google Scholar
  66. Schubert W, Steindorfer A, Button EA. Displacement monitoring in tunnels—an overview. Felsbau. 2002;20(2):7–15.Google Scholar
  67. Sharma KG, Pande GN. Stability of rock masses reinforced by passive, fully-grouted bolts. Int J Rock Mech Min Sci Geomech Abstr. 1988;25(5):273–85.CrossRefGoogle Scholar
  68. Spang K, Egger P. Action of fully-grouted bolts in jointed rock and factors of influence. Rock Mech Rock Eng. 1990;23(2):201–29.CrossRefGoogle Scholar
  69. ST. John CM, Van Dillen DE. Rockbolts: a new numerical representation and its application in tunnel design. In: Proceedings of the 24th US symposium on rock mechanics. New York: AEG; 1983. p. 13–25.Google Scholar
  70. Stheeman WH. A practical solution to cable bolting problems at the Tsumeb Mine. CIM Bull. 1982;75(838):65–77.Google Scholar
  71. Stillborg B. Experimental investigation of steel cable for rock reinforcement in hard rock. Ph.D. thesis, Lulea University of Technology, Sweden; 1984.Google Scholar
  72. Stillborg B. Professional users handbook for rock bolting. 2nd edition. Clausthal-Zellerfeld: Trans Tech Publications Limited; 1994.Google Scholar
  73. Swoboda G, Marence M. FEM modelling of rockbolts. In: Proceedings of the computer methods and advance in geomechanics. Rotterdam: AA Balkema; 1991. p. 1515–20.Google Scholar
  74. Swoboda G, Marence M. Numerical modelling of rock bolts in intersection with fault system. In: Proceedings of the numerical models in geomechanics, NUMOG 5. Swansea: Pineridge Press Ltd.;1992. p. 729–38.Google Scholar
  75. Timoshenko S. Theory of plates and shells. New York: McGraw-Hill; 1940.zbMATHGoogle Scholar
  76. Weerasinghe RB, Littlejohn GS. Load transfer and failure of anchorages in weak mudstone. In: Littlejohn GS, editor. Proceedings of the conference on ground anchorages and anchored structures. London: Thomas Telford, Institution of Civil Engineers (ICE); 1977. p. 23–4.Google Scholar
  77. Windsor CR. Rock reinforcement systems. Int J Rock Mech Min Sci. 1997;34(6):919–51.CrossRefGoogle Scholar
  78. Woods RI, Barkhordari K. The influence of bond stress distribution on ground anchor design. In: Littlejohn GS, editor. Proceedings of the conference on ground anchorages and anchored structures. London: Thomas Telford, Institution of Civil Engineers (ICE); 1997. p. 55–65.Google Scholar
  79. Yazici S, Kaiser PK. Bond strength of grouted cable bolts. Int J Rock Mech Min Sci Geomech Abstr. 1992;29(3):279–92.CrossRefGoogle Scholar
  80. Zachow R. Dimensionierung zweischaliger Thnnel in Fels auf der Grund lage von in-situ Messungen (Dimensioning of bicoque tunnels in rock masses based on in situ measurements). Technical report 16. Hannover: University of Hannover; 1995 (in German).Google Scholar
  81. Zienkiewicz OC, Pande GN. Time dependent multi-laminated model of rocks—a numerical study of deformation and failure of jointed rock masses. Int J Numer Anal Methods Geomech. 1976;1(3):219–47.CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of Water Resources and Hydropower EngineeringWuhan UniversityWuhanP.R. China

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