Geomechanics and Engineering

  • 제8권3호
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  • Pages.441-460
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  • 2015
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  • 2005-307X(pISSN)
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  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Theoretical determination of stress around a tensioned grouted anchor in rock

  • Showkati, Alan (Faculty of Mining and Metallurgical Engineering, Amirkabir University of Technology) ;
  • Maarefvand, Parviz (Faculty of Mining and Metallurgical Engineering, Amirkabir University of Technology) ;
  • Hassani, Hossein (Faculty of Mining and Metallurgical Engineering, Amirkabir University of Technology)
  • 투고 : 2014.01.29
  • 심사 : 2014.12.20
  • 발행 : 2015.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

A new theoretical approach for analysis of stress around a tensioned anchor in rock is presented in this paper. The solution has been derived for semi-infinite elastic rock and anchor and for plane strain conditions. The method considers both the anchor head bearing plate and its grouted bond length embedded in depth. The solution of the tensioned rock anchor problem is obtained by superimposing the solutions of two simpler but fundamental problems: A distributed load applied at a finite portion (bearing plate area) of the rock surface and a distributed shear stress applied at the anchor-rock interface along the bond length. The solution of the first problem already exists and the solution of the shear stress distributed along the bond length is found in this study. To acquire a deep understanding of the stress distribution around a tensioned anchor in rock, an illustrative example is solved and stress contours are drawn for stress components. In order to verify the results obtained by the proposed solution, comparisons are made with finite difference method (FDM) results. Very good agreements are observed for the teoretical results in comparison with FDM.

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참고문헌

  1. Akgün, H. and Koçkar, M.K. (2004), "Design of anchorage and assessment of the stability of openings in silty-sandy limestone: A case study in Turkey", Int. J. Rock Mech. Min. Sci., 41(1), 37-49. https://doi.org/10.1016/S1365-1609(03)00073-X
  2. Bobet, A. (2006), "A simple method for analysis of point anchored rockbolts in circular tunnels in elastic ground", Rock Mech. Rock. Eng., 39(4), 315-338. https://doi.org/10.1007/s00603-005-0066-3
  3. Bobet, A. and Einstein, H.H. (2011), "Tunnel reinforcement with rockbolts", Tunn. Undergr. Space Technol., 26(1), 100-123. https://doi.org/10.1016/j.tust.2010.06.006
  4. Brown, E.T. (1974), "Fracture of rock under uniform biaxial compression", Proceedings of the 3rd International Congress on Rock Mechanics, Denver, CO, USA, September, pp. 111-117.
  5. Brown, E.T. (Ed.) (1987), Analytical and Computational Methods in Engineering Rock Mechanics, Allen & Unwin, London, UK.
  6. Bruce, D.A. (1992), "Prestressed anchorages for retaining structures applications and construction", ADSC Boston Earth Retention Seminar, Boston, MA, USA.
  7. Bruce, D.A. (1997), "The stabilization of concrete dams by tensioned rock anchors: the state of American practice", Proceedings of the International Conference on Ground Anchorages and Anchored Structures, London, UK, March.
  8. Brudent, O.L. (1990), "Analysis and design of anchorage zones in post tensioned concrete bridges", Doctor of Philosophy, University of Texas, Austin, TX, USA.
  9. Culver, R.S. and Jorstad, T. (1967), "Fracturing around a rock bolt anchor", Proceedings of the 9th US Symposium on Rock Mechanics (USRMS), Golden, CO, USA, April.
  10. Danziger, F.A.B., Danziger, B.R. and Pacheco, M.P. (2006), "The simultaneous use of piles and prestressed anchors in foundation design", J. Eng. Geol., 87(3-4), 163-177. https://doi.org/10.1016/j.enggeo.2006.06.003
  11. Farmer, I.W. (1975), "Stress distribution along a resin grouted rock anchor", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 12(11), 347-351. https://doi.org/10.1016/0148-9062(75)90168-0
  12. Gander, W. and Gautschi, W. (2000), "Adaptive quadrature - Revisited", BIT Numer. Math., 40(1), 84-101. https://doi.org/10.1023/A:1022318402393
  13. Gao, F. and Kang, H. (2008), "Effect of pre-tensioned rock bolts on stress redistribution around a roadway-insight from numerical modeling", J. China Univ. Min. Technol., 18(4), 509-515. https://doi.org/10.1016/S1006-1266(08)60285-0
  14. Hanna, T.H. (1982), Foundations in Tension-Ground Anchors, Trans Tech Publications, Clausthal-Zellerfeld, Germany.
  15. Hobst, L. and Zajic, J. (1977), Anchoring in Rock, Elsevier, Amsterdam, Netherlands.
  16. Hseuh, C.H. (1995), "Modeling of elastic stress transfer in fiber-reinforced composites", Trends Polym. Sci., 10, 336.
  17. Itasca Consulting Group, Inc. (2005), FLAC User's Guide Manual, (Ver. 5.0), 111 Third Avenue South, Suite 450, Minneapolis, MN 55401, USA.
  18. Kim, N.K., Park. J.S. and Kim. S.K. (2007), "Numerical simulation of ground anchors", J. Comput. Geotech., 34(6), 498-507. https://doi.org/10.1016/j.compgeo.2006.09.002
  19. Li, C. and Stillborg, B. (1999), "Analytical models for rock bolts", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 36(8), 1013-1029. https://doi.org/10.1016/S1365-1609(99)00064-7
  20. Littlejohn, S. (1993), "Overview of rock anchorages", (Hudson, J.A. Ed.), Comprehensive Rock engineering, Principles, Practice and Projects, Pergamon, Volume 4, pp. 413-450.
  21. Littlejohn, G.S., Norton, P.J. and Turner, M.J. (1977), "A study of rock slope reinforcement at Westfield (Scotland) open pit and the effect of blasting on prestressed anchors", Proceeding of the Conference on Rock Engineering, University of Newcastle upon Tyne, UK, April.
  22. Mathworks, Co. (2010), Matlab Software, (Ver. R2010a), Natick, MA, USA.
  23. McCartney, L.N. (1989), "New theoretical model of stress transfer between fiber and matrix in a uniaxially fiber-reinforced composite", Proceeding of the Royal Society, London, UK.
  24. Mindlin, R.D. (1936), "Force at a point in the interior of a semi-infinite solid", J. Phys., 7(5),195-202.
  25. Muskhelishvili, N.I. (1975), Some Basic Problem of the mathematical Theory of Elasticity, (2nd Edition), Noordhoff International Publishing, Netherlands.
  26. Narin, J.A. and Mendels, D.A. (1996), "On the use of planar shear-lag methods for stress-transfer analysis of multilayered composites", Mech. Mater., 33(6), 335-362. https://doi.org/10.1016/S0167-6636(01)00056-4
  27. Nitzsche, R.N. and Haas, C.J. (1976), "Installation induced stresses for grouted roof bolts", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 13(1), 17-24. https://doi.org/10.1016/0148-9062(76)90223-0
  28. Papanastassopoulou, F. (1983), "Investigation of effect of rock bolts on stress distribution around underground excavations", Proceeding of the International Symposium on Rock Bolting, Abisko, Sweden, August-September.
  29. Poulos, H.G. and Davis, E.H. (1974), Elastic Solutions for Soil and Rock Mechanics, John Wiley and Sons, New York, NY, USA.
  30. Russell, J.E. (1968), "Stress distribution around rock bolts: Elastic stresses", Proceedings of the 10th US Symposium on Rock Mechanics (USRMS), Austin, TX, USA, May.
  31. Sabatini, P.J., Pass, D.G. and Bachus, R.C. (1999), "Ground Anchors and Anchored Systems", Office of Bridge Technology Federal Highway Administration (FHWA), Report No. FHWA-IF-99-015.
  32. Sadd, M.H. (2005), Elasticity; Theory, Application, and Numerics, Elsevier Butterworth-Heinemann, Burlington, MA, USA.
  33. Sagaseta, C., Sanchez. J.M. and Canizal J. (2001), "A general analytical solution for the required anchor force in rock slopes with toppling failure", Int. J. Rock Mech. Min. Sci., 38(3), 421-435. https://doi.org/10.1016/S1365-1609(01)00011-9
  34. Saliman, R. and Schaefer, R. (1968), "Anchored footings for transmission towers", ASCE Annual Meeting and National Meeting on Structural Engineering, Pittsburgh, PA, USA, September-October.
  35. Sanders, D.H. and Breen, J.E. (1997), "Tensioned anchorage zones with single straight concentric anchorages", ACI Struct. J., 94(2), 146-158.
  36. Timoshenko, S.P. and Goodier, J.N. (1970), Theory of Elasticity, (3rd Edition), McGraw, New York, NY, USA.
  37. Tonon, F. and Asadollahi, P. (2008), "Validation of general single rock block stability analysis (BS3D) for wedge failure", Int. J. Rock Mech. Min. Sci., 45(4), 627-637. https://doi.org/10.1016/j.ijrmms.2007.08.014
  38. Wijk, G.A. (1978), "Theoretical remark on the stress field around prestressed rock bolts", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 15(6), 289-294. https://doi.org/10.1016/0148-9062(78)91469-9
  39. Windsor, C.R. (1997), "Rock reinforcement systems", Int. J. Rock Mech. Min. Sci., 34(6), 919-951. https://doi.org/10.1016/S1365-1609(97)80004-4
  40. Windsor, C.R. and Thompson, A.G. (1993), "Rock reinforcement-technology, testing, design and evaluation", (Hudson, J.A. Ed.), In: Comprehensive Rock Engineering, Principles, Practice and Projects, Pergamon, Volume 4, pp. 451-484.
  41. Wu, Y., Mao, X., Huang. J., Sun, F. and Yao, B. (2010), "Action mechanism of a mechanical end-anchorage bolt", J. Min. Sci. Technol., 20(4), 625-628.
  42. Wyllie, D.C. (2005), Foundations on Rock, (2nd Edition), Taylor & Francis e-Library.
  43. Yap, L.P. and Rodger, A.A. (1984), "A study of the behavior of vertical rock anchors using finite element method", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 21(2), 47-61.
  44. Zhao, J.L., Shen, S.H., Wang, L.B. and Chen, J. (2011), "A design approach for the interior anchorage zone of tensioned concrete structures", KSCE J. Civ. Eng., 15(3), 487-495. https://doi.org/10.1007/s12205-011-0835-3

피인용 문헌

  1. Theoretical solutions for displacement and stress of a circular opening reinforced by grouted rock bolt vol.11, pp.3, 2016, https://doi.org/10.12989/gae.2016.11.3.439
  2. Mechanical Effect Analysis and Comparative Site Tests on Surrounding Rock with Different Bolt Anchoring Lengths and Pre-tightening Forces pp.1573-1529, 2019, https://doi.org/10.1007/s10706-018-0678-5
  3. Pressure analysis in grouting and water pressure test to achieving optimal pressure vol.13, pp.4, 2015, https://doi.org/10.12989/gae.2017.13.4.685