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Pseudostatic analysis of bearing capacity of embedded strip footings in rock masses using the upper bound method

  • Saeed Shamloo (Geotechnical Engineering Group, Amirkabir Univercity of Technology) ;
  • Meysam Imani (Geotechnical Engineering Group, Amirkabir Univercity of Technology)
  • 투고 : 2022.06.01
  • 심사 : 2023.06.30
  • 발행 : 2023.08.25

초록

The present paper evaluates seismic bearing capacity of rock masses subjected to loads of strip footings using the upper bound method. A general formula was proposed to evaluate the seismic bearing capacity considering both the horizontal and vertical accelerations of the earthquake and the effects of footing embedment depth simultaneously. Modified Hoek-Brown failure criterion was employed for the rock mass. Some comparisons were made with the available solutions and the finite element numerical models to show the accuracy of the developed upper bound formulations. The obtained results show significant improvement compared to the other available solutions. By increasing the horizontal earthquake acceleration from 0.1 to 0.3, the bearing capacity was reduced by up to 39%, while the effect of the vertical earthquake acceleration depends on its direction. An upward acceleration in the range of zero to 0.2 results in an increase in the bearing capacity by up to 24%, while the downward earthquake acceleration has an adverse effect. Also, by increasing the embedment depth of the footing from zero to 5 times the footing width, the value of seismic bearing capacity was raised about 86%. The obtained results were presented as design tables for use in practical applications.

키워드

참고문헌

  1. Alencar, A.S., Galindo, R.A. and Svetlana, M. (2019), "Bearing capacity of foundation on rock mass depending on footing shape and interface roughness", Geomech. Eng., 18(4), 391-406. https://doi.org/10.12989/gae.2019.18.4.0391. 
  2. Alencar, A.S., Galindo, R.A. and Svetlana, M. (2020), "Bearing capacity of shallow foundations on the bilayer rock", Geomech. Eng., 21(1), 11-21. https://doi.org/10.12989/gae.2020.21.1.011. 
  3. AlKhafaji, H., Imani, M. and Fahimifar, A. (2020), "Ultimate bearing capacity of rock mass foundations subjected to seepage forces using modified Hoek-Brown criterion", Rock Mech. Rock Eng., 53, 251-268. http://doi.org/10.1007/s00603-019-01905-6. 
  4. Ausilio, E. and Zimmaro, P. (2015), "Displacement-based seismic design of a shallow strip footing positioned near the edge of a rock slope", Int. J. Rock Mech. Min. Sci., 76, 68-77. https://doi.org/10.1016/j.ijrmms.2015.02.010. 
  5. Beygi, M., Keshavarz, A., Abbaspour, M., Vali, R., Saberian, M. and Li, J. (2020), "Finite element limit analysis of the seismic bearing capacity of strip footing adjacent to excavation in c-φ soil", Geomech. Geoeng., https://doi.org/10.1080/17486025.2020.1728396. 
  6. Bindlish, A., Singh, M. and Samadhiya, N.K. (2012), "Ultimate bearing capacity of shallow foundations on jointed rock mass", Indian Geotech. J., 42(3), 169-178. https://doi.org/10.1007/s40098-012-0011-9. 
  7. Chen, B.H., Lou, W.J., Xu, X.Y. and Hu, R.Q. (2022), "Seismic bearing capacity of strip footing with nonlinear Mohr-Coulomb failure criterion", Int. J. Geomech., 22(10). https://doi.org/10.1061/(ASCE)GM.1943-5622.0002521. 
  8. Ghosh, S. and Debnath, L. (2017), "Seismic bearing capacity of shallow strip footing with coulomb failure mechanism using limit equilibrium method", Geotech. Geol. Eng., https://doi.org/10.1007/s10706-017-0268-y. 
  9. Hoek, E., Carranza, C. and Corkum, B. (2002), "Hoek-Brown failure criterion, 2002 edition", Proceedings of the NARMS-Tac, 267-273. https://doi.org/10.1016/0148-9062(74)91782-3. 
  10. Imani, M. and Aali, R. (2020), "Effects of embedment depth of foundations on ultimate bearing capacity of rock masses", Geotech. Geol. Eng., https://doi.org/10.1007/s10706-020-01452-w. 
  11. Imani, M., Fahimifar, A. and Sharifzadeh, M. (2012), "Upper bound solution for the bearing capacity of submerged jointed rock foundations", Rock Mech. Rock Eng., 45, 639-646. https://doi.org/10.1007/s00603-011-0215-9. 
  12. Johari, A., Hosseini, S.M. and Keshavarz, A. (2017), "Reliability analysis of seismic bearing capacity of strip footing by stochastic slip lines method", Comput. Geotech., 91, 203-217. https://doi.org/10.1016/j.compgeo.2017.07.019. 
  13. Jahani, M., Oulapour, M., Haghighi, A. (2018), "Evaluation of the Seismic Bearing Capacity of Shallow Foundations Located on the Two-Layered Clayey Soils", Iran J Sci Technol Trans Civ Eng. https://doi.org/10.1007/s40996-018-0122-3. 
  14. Keshavarz, A., Jahanandish, M. and Ghahramani, A. (2011), "Seismic bearing capacity analysis of reinforced soils by the method of stress characteristics", Iran J. Sci. Technol. Trans. Civ. Eng., 35(2), 185-197. https://doi.org/10.22099/IJSTC.2012.666. 
  15. Keshavarz, A., Fazeli, A. and Sadeghi, S. (2016), "Seismic bearing capacity of strip footings on rock masses using the HoekeBrown failure criterion", J. Rock Mech. Geotech. En.g, 8, 170-177. https://doi.org/10.1016/j.jrmge.2015.10.003. 
  16. Keshavarz, A. and Kumar, J. (2017), "Bearing capacity of foundations on rock mass using the method of characteristics", Int. J. Numer. Anal. Method. Geomech., 1-16. https://doi.org/10.1002/nag.2754. 
  17. Kumar, J. and Rahaman, O. (2020), "Lower bound limit analysis using power cone programming for solving stability problems in rock mechanics for generalized Hoek-Brown criterion", Rock Mech. Rock Eng., https://doi.org/10.1007/s00603-020-02099-y. 
  18. Li, C., Jiang, P. and Zhou, A. (2019), "Rigorous solution of slope stability under seismic action", Comput. Geotech., 109, 99-107. https://doi.org/10.1016/j.compgeo.2019.01.018. 
  19. MATLAB. (R2016a), https://www.mathworks.com. 
  20. Mao, N., Al-Bittar, T. and Soubra, A.H. (2012), "Probabilistic analysis and design of strip foundations resting on rocks obeying Hoek-Brown failure criterion", Int. J. Rock Mech. Min. Sci., 49, 45-58. https://doi.org/10.1016/j.ijrmm s.2011.11.005. 
  21. Meyerhof, G.G. (1951), "The ultimate bearing capacity of foundations", Geotechnique, 2(4), 301-332. https://doi.org/10.1680/geot.1951.2.4.301. 
  22. Phase2. Ver.8. (2011), www.rocscience.com.
  23. Prakoso, W.A. and Kulhawy, F.H. (2004), "Bearing capacity of strip footings on jointed rock masses", J. Geotech. Geoenviron. Eng., 130(12). https://doi.org/10.1061/(ASCE)1090-0241(2004)130:12(1347). 
  24. Roy, N. and Koul, S. (2022) "Effect of embedment depth on the seismic bearing capacity of strip footing in rock mass", Int. J. Geomech., 22(7), 06022010. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002463. 
  25. Saada, Z., Maghous, S. and Garnier, D. (2008), "Bearing capacity of shallow foundations on rocks obeying a modified Hoek-Brown failure criterion", Comput. Geotech., 35, 144-154. https://doi.org/10.1016/j.compg eo.2007.06.003. 
  26. Saada, Z., Maghous, S. and Garnier, D. (2011), "Seismic bearing capacity of shallow foundations near rock slopes using the generalized Hoek-Brown criterion", Int. J. Numer. Anal. Meth. Geomech., 35, 724-748. https://doi.org/10.1002/nag. 
  27. Shamloo, S., Imani, M. (2020), "Upper bound solution for the bearing capacity of rock masses considering the embedment depth", Ocean Eng., 218(108169). https://doi.org/10.1016/j.oceaneng.2020.108169. 
  28. Shamloo, S. and Imani, M. (2021), "Upper bound solution for the bearing capacity of two adjacent footings on rock masses", Comput. Geotech., 129(103855). https://doi.org/10.1016/j.compgeo.2020.103855. 
  29. Shinohara, T., Tateishi, T. and Kubo, K. (1960) "Bearing capacity of sandy soil for eccentric and inclined load and lateral resistance of single piles embedded in sandy soil", Proceedings of the 2nd World Conference on Earthquake Engineering. Tokyo. 
  30. Soubra, A.H. (1999), "Upper-bound solutions for bearing capacity of foundations", J. Geotech. Geoenviron. Eng., 125(1), 59-68. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:1(59). 
  31. Trautmann, C.H. and kulhawy, F.H. (1998), "Uplift Load-Displacement Behavior of Spread Foundations", J. Geotech. Eng. - ASCE, 114(2), 168-183. https://doi.org/10.1061/(ASCE)0733-9410 (1988) 114:2(168). 
  32. Wang, Y.J., Yin, J.H. and Chen, Z.Y. (2001), "Calculation of bearing capacity of a strip footing using an upper bound method", Int. J. Numer. Anal. Meth. Geomech., 25, 841-851. https://doi.org/10.1002/nag.151. 
  33. Wu, G., Zhao, H., Zhao, M. and Xiao, Y. (2020), "Undrained seismic bearing capacity of strip footings lying on two-layered slopes", Comput. Geotech., 122(103539). https://doi.org/10.1016/j.compgeo.2020.103539. 
  34. Yang, X.L. and Yin, J.H. (2005), "Upper bound solution for ultimate bearing capacity with a modified Hoek-Brown failure criterion", Int. J. Rock Mech. Min. Sci., 42, 550-560. https://doi.org/10.1016/j.ijrmms.2005.03.002. 
  35. Yang, X.L. (2009), "Seismic bearing capacity of a strip footing on rock slopes", Can Geotech. J., 46, 943-954. https://doi.org/10.1139/T09-038.