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Limit Analysis Solutions for Bearing Capacity of Ring Foundations on Rocks Using Hoek–Brown Failure Criterion

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A Correction to this article was published on 10 June 2021

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Abstract

In this paper, new limit analysis solutions for the bearing capacity of ring foundations on rock masses are presented, where the Hoek–Brown yield criterion is used as a failure criterion for rock masses. The lower and upper bound finite element limit analysis is employed to derive the bearing capacity solutions of ring foundations on rock masses. The ring foundation has internal and external radii. The considered dimensionless parameters include the ratio between the internal radius and the external radius, the yield parameter, and the geological strength index of rock, where the effects of these dimensionless parameters on the bearing capacity factor are investigated. It is found that a high yield parameter or a high geological strength index yields a high value of the bearing capacity factor. When the ratio between the internal radius and the external radius is around 0.25, the bearing capacity factor becomes the largest. The collapse mechanisms of this problem are also examined and discussed in the present study.

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References

  1. Hoek E, Brown ET (1980) Empirical strength criterion for rock masses. J Geotech Eng Div 106(9):1013–1035

    Article  Google Scholar 

  2. Hoek E, Carranza-Torres C, Corkum B (2002) Hoek–Brown failure criterion—2002 edition. In: Proceedings of the North American rock mechanics society meeting in Toronto, Canada

  3. Serrano A, Olalla C (1994) Ultimate bearing capacity of rock masses. Int J Rock Mech Mining Sci Geomech Abstr 31(2):93–106

    Article  Google Scholar 

  4. Serrano A, Olalla C (1998) Ultimate bearing capacity of an anisotropic discontinuous rock mass, part I: basic modes of failure. Int J Rock Mech Min Sci 35(3):301–324

    Article  Google Scholar 

  5. Serrano A, Olalla C (1998) Ultimate bearing capacity of an anisotropic discontinuous rock mass, part II: determination procedure. Int J Rock Mech Min Sci 35(3):325–348

    Article  Google Scholar 

  6. Yang XL, Yin JH (2005) Upper bound solution for ultimate bearing capacity with modified Hoek-Brown failure criterion. Int J Rock Mech Min Sci 42:550–560

    Article  Google Scholar 

  7. Merifield RS, Lyamin AV, Sloan SW (2006) Limit analysis solutions for the bearing capacity of rock masses using the generalized Hoek-Brown criterion. Int J Rock Mech Min Sci 43(6):920–937

    Article  Google Scholar 

  8. Saada Z, Maghous S, Garnier D (2008) Bearing capacity of shallow foundations on rocks obeying a modified Hoek-Brown failure criterion. Comput Geotech 35:144–154

    Article  Google Scholar 

  9. Chihi O, Saada Z (2020) Bearing capacity of strip footing on rock under inclined and eccentric load using the generalized Hoek-Brown criterion. Eur J Environ Civ Eng. https://doi.org/10.1080/19648189.2020.1757513

    Article  Google Scholar 

  10. Keawsawasvong S, Thongchom C, Likitlersuang S (2020) Bearing capacity of strip footing on Hoek-Brown rock mass subjected to eccentric and inclined loading. Transport Infrastruct Geotechnol. https://doi.org/10.1007/s40515-020-00133-8

    Article  Google Scholar 

  11. Clausen J (2013) Bearing capacity of circular footings on a Hoek-Brown material. Int J Rock Mech Min Sci 57:34–41

    Article  Google Scholar 

  12. Chakraborty M, Kumar J (2015) Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis. Comput Geotech 70:138–149

    Article  Google Scholar 

  13. Keshavarz A, Kumar J (2018) Bearing capacity of foundations on rock mass using the method of characteristics. Int J Numer Anal Meth Geomech 42:542–557

    Article  Google Scholar 

  14. Kumar J, Mohapatra D (2017) Lower-bound finite elements limit analysis for Hoek-Brown materials using semidefinite programming. J Eng Mech 143(9):04017077

    Article  Google Scholar 

  15. Ukritchon B, Keawsawasvong S (2018) Three-dimensional lower bound finite element limit analysis of Hoek-Brown material using semidefinite programming. Comput Geotech 104:248–270

    Article  Google Scholar 

  16. Kumar J, Ghosh P (2005) Bearing capacity factor Nγ for ring footings using the method of characteristics. Can Geotech J 42:1474–1484

    Article  Google Scholar 

  17. Keshavarz A, Kumar J (2017) Bearing capacity computation for a ring foundation using the stress characteristics method. Comput Geotech 89:33–42

    Article  Google Scholar 

  18. Zhao L, Wang JH (2008) Vertical bearing capacity for ring footings. Comput Geotech 35:292–304

    Article  Google Scholar 

  19. Benmebarek S, Remadna MS, Benmebarek N, Belounar L (2012) Numerical evaluation of the bearing capacity factor of ring footings. Comput Geotech 44:132–138

    Article  Google Scholar 

  20. Kumar J, Chakraborty M (2015) Bearing capacity factors for ring foundations. J Geotechn Geoenviron Eng 141:06015007

    Article  Google Scholar 

  21. Benmebarek S, Saifi I, Benmebarek N (2017) Undrained vertical bearing capacity factors for ring shallow footings. Geotech Geol Eng 35:1–10

    Article  Google Scholar 

  22. Lee JK, Jeong S, Lee S (2016) Undrained bearing capacity factors for ring footings in heterogeneous soil. Comput Geotech 75:103–111

    Article  Google Scholar 

  23. Lee JK, Jeong S, Shang JQ (2016) Undrained bearing capacity of ring foundations on two-layered clays. Ocean Eng 119:47–57

    Article  Google Scholar 

  24. Yang C, Zhu Z, Xiao Y (2020) Bearing capacity of ring foundations on sand overlying clay. Appl Sci 10:4675

    Article  Google Scholar 

  25. Das PP, Khatri VN, Dutta RK (2019) Bearing capacity of ring footing on weak sand layer overlying a dense sand deposit. Geomech Geoeng. https://doi.org/10.1080/17486025.2019.1664775

    Article  Google Scholar 

  26. Khatri VN, Kumar J, Das PP (2020) Bearing capacity of ring footings placed on dense sand underlain by a loose sand layer. Eur J Environ Civ Eng. https://doi.org/10.1080/19648189.2020.1805643

    Article  Google Scholar 

  27. Sharma V, Kumar A (2017) Strength and bearing capacity of ring footings resting on fibre-reinforced sand. Int J Geosynth Ground Eng 3:9

    Article  Google Scholar 

  28. Benmebarek S, Remadna A, Benmebarek N (2018) Numerical modelling of stone column installation effects on performance of circular footing. Int J Geosynth Ground Eng 4:23

    Article  Google Scholar 

  29. Biswas A, Ansari MA, Dash SK, Krishna AM (2015) Behavior of geogrid reinforced foundation systems supported on clay subgrades of different strengths. Int J Geosynth Ground Eng 1:20

    Article  Google Scholar 

  30. Badakhshan E, Noorzad A (2017) A simplified method for prediction of ultimate bearing capacity of eccentrically loaded foundation on geogrid reinforced sand bed. Int J Geosynth Ground Eng 3:14

  31. Sloan SW (2013) Geotechnical stability analysis. Géotechnique 63(7):531–572

    Article  Google Scholar 

  32. Drucker DC, Prager W, Greenberg HJ (1952) Extended limit design theorems for continuous media. Q Appl Math 9:381–389

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  34. Krabbenhoft K, Lyamin A, Krabbenhoft J (2015) Optum computational engineering (OptumG2). www.optumce.com

  35. Ciria H, Peraire J, Bonet J (2008) Mesh adaptive computation of upper and lower bounds in limit analysis. Int J Numer Meth Eng 75:899–944

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The first author would like to acknowledge Thammasat School of Engineering, Thammasat University, for the graduate scholarship.

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Authors and Affiliations

  1. Department of Civil Engineering, Thammasat School of Engineering, Thammasat University, Pathumthani, 12120, Thailand

    Wittawat Yodsomjai & Suraparb Keawsawasvong

  2. Faculty of Civil Engineering, Ho Chi Minh City University of Technology, (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, Viet Nam

    Van Qui Lai

  3. Vietnam National University Ho Chi Minh City (VNU-HCM), Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam

    Van Qui Lai

Authors
  1. Wittawat Yodsomjai
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  2. Suraparb Keawsawasvong
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  3. Van Qui Lai
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Contributions

WY acquired methodology, software and contributed to the investigation and data curation. SK acquired supervision, methodology, and contributed to conceptualization, writing—original draft. VQL provided resources and contributed to writing—review and editing.

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Correspondence to Suraparb Keawsawasvong.

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Yodsomjai, W., Keawsawasvong, S. & Lai, V.Q. Limit Analysis Solutions for Bearing Capacity of Ring Foundations on Rocks Using Hoek–Brown Failure Criterion. Int. J. of Geosynth. and Ground Eng. 7, 29 (2021). https://doi.org/10.1007/s40891-021-00281-y

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