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A comparative study on the estimation of ultimate bearing capacity of rock masses using finite element and limit equilibrium methods

Year 2024, Issue: 056, 82 - 93, 31.03.2024

Serdar Koltuk

https://doi.org/10.59313/jsr-a.1420333

Abstract

Most rock masses are excellent foundation materials due to their bearing capacities of MPa. However, the ultimate bearing capacity of rock masses should be accurately estimated in the design of structures with high foundation loads. In this study, the ultimate bearing capacities of a strip footing built on rock masses with different geotechnical properties are determined using the finite element method (FEM) and the failure criterion of Hoek & Brown. The results of FE-analyses are compared to those obtained from the limit equilibrium methods (LEM) in the literature. It has been shown that the FEM with associated flow rule and Terzaghi`s limit equilibrium method give similar failure surfaces for most cases, and the ratio of ultimate bearing capacities determined according to the Terzaghi´s method to FEM varies between 1.5 and 4. In cases, in which the failure surfaces obtained from both methods differ, this ratio can rise up to 11.aring capacities determined according to the Terzaghi´s method to FEM varies between 1.5 and 4. In cases, in which the failure surfaces obtained from both methods differ, this ratio can rise up to 11.

Keywords

Ultimate Bearing Capacity Rock Masses Finite Element Method Limit Equilibrium Method

References

  • [1] K. Terzaghi, Theoretical soil mechanics. New York, USA: John Wiley & Sons, 1943.
  • [2] D.C. Wyllie, Foundations on Rock. London: E & FN Spon and USA and Canada: Routledge, 1999.
  • [3] A. Serrano, C. Ollala, and J. Gonzalez, “Ultimate bearing capacity of rock masses based on the modifed Hoek Brown criterion,” International Journal of Rock Mechanics & Mining Sciences, vol. 37, no. 6, pp. 1013–1018, September 2000, doi:10.1016/S1365-1609(00)00028-9.
  • [4] X. Yang and J.H. Yin, “Upper bound solution for ultimate bearing capacity with a modified Hoe-Brown failure Criterion,” International Journal of Rock Mechanics & Mining Sciences, vol. 42, no. 4, pp. 550–560, June 2005, doi: 10.1016/j.ijrmms.2005.03.002.
  • [5] R.S. Merifeld, A.V. Lyamin, and S.W. Sloan, “Limit analysis solutions for the bearing capacity of rock masses using the generalised Hoek-Brown criterion,” International Journal of Rock Mechanics & Mining Sciences, vol. 43, no. 6, pp. 920–937, September 2006, doi: 10.1016/j.ijrmms.2006.02.001.
  • [6] Z. Saada, S. Maghous, and D. Garnier, “Bearing capacity of shallow foundations on rocks obeying a modified Hoek–Brown failure criterion,” Computers and Geotechnics, vol. 35, no. 2, pp. 144-154, March 2008, doi: 10.1016/j.compgeo.2007.06.003.
  • [7] Eurocode 7, Geotechnical Design–Part 1: General Rules. CEN, Brussels: 2004.
  • [8] J.E. Bowles, Foundation Analysis and Design. Singapore: McGraw Hill, 1996.
  • [9] E. Hook, C. Carranza-Torres, and B. Corkun, “Hoek-Brown failure criterion-2002 edition,” in Proc. of the North American rock mechanics society meeting, 2002, October 267-273, 2002. [Online]. Available: https://www.rocscience.com/assets/resources/learning/hoek/Hoek-Brown-Failure-Criterion-2002.pdf.
  • [10] E. Hoek and E.T. Brown, “The Hoek-Brown failure criterion and GSI-2018 edition,” Journal of Rock Mechanics and Geotechnical Engineering, vol. 11, no. 3, pp. 445-463, June 2019, doi: 10.1016/j.jrmge.2018.08.001.
  • [11] T. Miranda, F. Martins, and N. Araujo, “Design of spread foundations on rock masses according to Eurocode 7,” in 12th ISRM Congress, 2011, pp. 1959-1962, doi: 10.1201/b11646-373.
  • [12] A.H. Javid, A. Fahimifar, and M. Imani, “Numerical investigation on the bearing capacity of two interfering strip footings resting on a rock mass,” Computers and Geotechnics, vol. 69, pp. 514-528, September 2015, doi: 10.1016/j.compgeo.2015.06.005.
  • [13] M. Mansouri, M. Imani, and A. Fahimifar, “Ultimate bearing capacity of rock masses under square and rectangular footings,” Computers and Geotechnics, 111, pp. 1-9, July 2019, doi: 10.1016/j.compgeo.2019.03.002.
  • [14] S. Shamloo and M. Imani, “Upper bound solution for the bearing capacity of rock masses considering the embedment depth,” Ocean Engineering, vol. 218, no. 6, December 2020, doi: 10.1016/j.oceaneng.2020.108169.
  • [15] G. Wu, M. Zhao, R. Zhang, and G. Liang, “Ultimate bearing capacity of eccentrically loaded strip footings above voids in rock masses,” Computers and Geotechnics, vol. 218, December 2020, doi: 10.1016/j.compgeo.2020.103819.
  • [16] H. Chen, H. Zhu, and L. Zhang, “An analytical approach to the ultimate bearing capacity of smooth and rough strip foundations on rock mass considering three-dimensional (3D) strength,” Computers and Geotechnics, vol. 149, no. 3, September 2022, doi: 10.1016/j.compgeo.2022.104865.
  • [17] M. Ranjbarnia, F. Zarei, and M. Goudarzy, “Probabilistic Analysis of Bearing Capacity of Square and Strip Foundations on Rock Mass by the Response Surface Methodology,” Rock Mechanics and Rock Engineering, 56, pp. 343–362, vol. 56, October 2022, doi: 10.1007/s00603-022-03090-5.
  • [18] S. Das and D. Chakraborty, “Effect of eccentric and inclined loading on the bearing capacity of strip footing placed on rock mass,” Journal of Mountain Science, vol. 21, pp. 292–312, January 2024, doi: 10.1007/s11629-023-8312-2.
  • [19] H. Chen, H. Zhu, and L. Zhang, “Semi-analytical solution for ultimate bearing capacity of smooth and rough circular foundations on rock considering three-dimensional strength,” International Journal for Numerical and Analytical Methods in Geomechanics, February 2024, doi: 10.1002/nag.3699.
  • [20] Plaxis 2D, Delft: Plaxisbv, 2019.
  • [21] M. Singh, M.N. Viladkar, P.S. Shekhawat, K. Tripathi, and M. Amin, “Bearing capacity of strip footings on jointed rock mass,” Arabian Journal of Geosciences, vol. 15, September 2022, doi: 10.1007/s12517-022-10841-9.
  • [22] B.M. Das, Principles of Foundation Engineering. Boston, USA: Cengage Learning, 2014.
  • [23] RocData, version 5.0, Toronto: Rocscience Inc., 2019.

Year 2024, Issue: 056, 82 - 93, 31.03.2024

Serdar Koltuk

https://doi.org/10.59313/jsr-a.1420333

Abstract

References

  • [1] K. Terzaghi, Theoretical soil mechanics. New York, USA: John Wiley & Sons, 1943.
  • [2] D.C. Wyllie, Foundations on Rock. London: E & FN Spon and USA and Canada: Routledge, 1999.
  • [3] A. Serrano, C. Ollala, and J. Gonzalez, “Ultimate bearing capacity of rock masses based on the modifed Hoek Brown criterion,” International Journal of Rock Mechanics & Mining Sciences, vol. 37, no. 6, pp. 1013–1018, September 2000, doi:10.1016/S1365-1609(00)00028-9.
  • [4] X. Yang and J.H. Yin, “Upper bound solution for ultimate bearing capacity with a modified Hoe-Brown failure Criterion,” International Journal of Rock Mechanics & Mining Sciences, vol. 42, no. 4, pp. 550–560, June 2005, doi: 10.1016/j.ijrmms.2005.03.002.
  • [5] R.S. Merifeld, A.V. Lyamin, and S.W. Sloan, “Limit analysis solutions for the bearing capacity of rock masses using the generalised Hoek-Brown criterion,” International Journal of Rock Mechanics & Mining Sciences, vol. 43, no. 6, pp. 920–937, September 2006, doi: 10.1016/j.ijrmms.2006.02.001.
  • [6] Z. Saada, S. Maghous, and D. Garnier, “Bearing capacity of shallow foundations on rocks obeying a modified Hoek–Brown failure criterion,” Computers and Geotechnics, vol. 35, no. 2, pp. 144-154, March 2008, doi: 10.1016/j.compgeo.2007.06.003.
  • [7] Eurocode 7, Geotechnical Design–Part 1: General Rules. CEN, Brussels: 2004.
  • [8] J.E. Bowles, Foundation Analysis and Design. Singapore: McGraw Hill, 1996.
  • [9] E. Hook, C. Carranza-Torres, and B. Corkun, “Hoek-Brown failure criterion-2002 edition,” in Proc. of the North American rock mechanics society meeting, 2002, October 267-273, 2002. [Online]. Available: https://www.rocscience.com/assets/resources/learning/hoek/Hoek-Brown-Failure-Criterion-2002.pdf.
  • [10] E. Hoek and E.T. Brown, “The Hoek-Brown failure criterion and GSI-2018 edition,” Journal of Rock Mechanics and Geotechnical Engineering, vol. 11, no. 3, pp. 445-463, June 2019, doi: 10.1016/j.jrmge.2018.08.001.
  • [11] T. Miranda, F. Martins, and N. Araujo, “Design of spread foundations on rock masses according to Eurocode 7,” in 12th ISRM Congress, 2011, pp. 1959-1962, doi: 10.1201/b11646-373.
  • [12] A.H. Javid, A. Fahimifar, and M. Imani, “Numerical investigation on the bearing capacity of two interfering strip footings resting on a rock mass,” Computers and Geotechnics, vol. 69, pp. 514-528, September 2015, doi: 10.1016/j.compgeo.2015.06.005.
  • [13] M. Mansouri, M. Imani, and A. Fahimifar, “Ultimate bearing capacity of rock masses under square and rectangular footings,” Computers and Geotechnics, 111, pp. 1-9, July 2019, doi: 10.1016/j.compgeo.2019.03.002.
  • [14] S. Shamloo and M. Imani, “Upper bound solution for the bearing capacity of rock masses considering the embedment depth,” Ocean Engineering, vol. 218, no. 6, December 2020, doi: 10.1016/j.oceaneng.2020.108169.
  • [15] G. Wu, M. Zhao, R. Zhang, and G. Liang, “Ultimate bearing capacity of eccentrically loaded strip footings above voids in rock masses,” Computers and Geotechnics, vol. 218, December 2020, doi: 10.1016/j.compgeo.2020.103819.
  • [16] H. Chen, H. Zhu, and L. Zhang, “An analytical approach to the ultimate bearing capacity of smooth and rough strip foundations on rock mass considering three-dimensional (3D) strength,” Computers and Geotechnics, vol. 149, no. 3, September 2022, doi: 10.1016/j.compgeo.2022.104865.
  • [17] M. Ranjbarnia, F. Zarei, and M. Goudarzy, “Probabilistic Analysis of Bearing Capacity of Square and Strip Foundations on Rock Mass by the Response Surface Methodology,” Rock Mechanics and Rock Engineering, 56, pp. 343–362, vol. 56, October 2022, doi: 10.1007/s00603-022-03090-5.
  • [18] S. Das and D. Chakraborty, “Effect of eccentric and inclined loading on the bearing capacity of strip footing placed on rock mass,” Journal of Mountain Science, vol. 21, pp. 292–312, January 2024, doi: 10.1007/s11629-023-8312-2.
  • [19] H. Chen, H. Zhu, and L. Zhang, “Semi-analytical solution for ultimate bearing capacity of smooth and rough circular foundations on rock considering three-dimensional strength,” International Journal for Numerical and Analytical Methods in Geomechanics, February 2024, doi: 10.1002/nag.3699.
  • [20] Plaxis 2D, Delft: Plaxisbv, 2019.
  • [21] M. Singh, M.N. Viladkar, P.S. Shekhawat, K. Tripathi, and M. Amin, “Bearing capacity of strip footings on jointed rock mass,” Arabian Journal of Geosciences, vol. 15, September 2022, doi: 10.1007/s12517-022-10841-9.
  • [22] B.M. Das, Principles of Foundation Engineering. Boston, USA: Cengage Learning, 2014.
  • [23] RocData, version 5.0, Toronto: Rocscience Inc., 2019.
There are 23 citations in total.

Details

Primary Language English
Subjects Civil Geotechnical Engineering
Journal Section Research Articles
Authors

Serdar Koltuk 0000-0002-6214-0848

Publication Date March 31, 2024
Submission Date January 15, 2024
Acceptance Date February 27, 2024
Published in Issue Year 2024 Issue: 056

Cite

IEEE S. Koltuk, “A comparative study on the estimation of ultimate bearing capacity of rock masses using finite element and limit equilibrium methods”, JSR-A, no. 056, pp. 82–93, March 2024, doi: 10.59313/jsr-a.1420333.
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