Structural Engineering and Mechanics

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Seismic response of a rigid foundation embedded in a viscoelastic soil by taking into account the soil-foundation interaction

  • Received : 2015.08.04
  • Accepted : 2016.03.26
  • Published : 2016.06.10
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Abstract

This study analyses the seismic response of a three-dimensional (3-D) rigid massless square foundation resting or embedded in a viscoelastic soil limited by rigid bedrock. The foundation is subjected to harmonic oblique seismic waves P, SV, SH and R. The key step is the characterization of the soil-foundation interaction by computing the impedance matrix and the input motion matrix. A 3-D frequency boundary element method (BEM) in conjunction with the thin layer method (TLM) is adapted for the seismic analysis of the foundation. The dynamic response of the rigid foundation is solved from the wave equations by taking into account the soil-foundation interaction. The solution is formulated using the frequency BEM with the Green's function obtained from the TLM. This approach has been applied to analyze the effect of soilstructure interaction on the seismic response of the foundation as a function of the kind of incident waves, the angles of incident waves, the wave's frequencies and the embedding of foundation. The parametric results show that the non-vertical incident waves, the embedment of foundation, and the wave's frequencies have important impact on the dynamic response of rigid foundations.

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References

  1. Aubry, D. and Clouteau, D. (1992), "A subdomain approach to dynamic soil-structure interaction", Davidovic, V. and Clough, R., Recent AdvancesEarthquake Engineering and Structural Dynamics, Ouest editions/AFPS, Nantes, France.
  2. Akino, K., Ohtsuka, Y., Fukuoka, A. and Ishida, K. (1996), "Experimental studies on embedment effects on dynamic soil-structure interaction", Proceedings of the11th World Conference on Earthquake Engineering, Acapulco, Mexico, June.
  3. Apsel, R.J. and Luco, J.E. (1987), "Impedance functions for foundations embedded in layered medium: An integral equation approach", Earthq. Eng. Struct. Dyn., 15, 213-231. https://doi.org/10.1002/eqe.4290150205
  4. Beskos, D.E. (1987), "Boundary element methods in dynamic analysis", Appl. Mech. Rev., 40, 1-23. https://doi.org/10.1115/1.3149529
  5. Boumekik, A. (1985), "Fonctions impedances d'une fondation vibrante en surface ou partiellement encastree dans un sol multicouche", Ph.D. Dissertation, Free University of Bruxelles, Bruxelles.
  6. Celebi, E., Firat, S. and Cankaya, I., (2006), "The evaluation of impedance functions in the analysis of foundations vibrations using boundary element method", Appl. Math. Comput., 173, 636-667. https://doi.org/10.1016/j.amc.2005.04.006
  7. Chen, S.S. and Hou, J.G. (2015), "Response of circular flexible foundations subjected to horizontal and rocking motions", Soil Dyn. Earthq. Eng., 69, 182-195. https://doi.org/10.1016/j.soildyn.2014.10.022
  8. Fujimori, T., Tsundoa, T., Izumi, M. and Akino, K., (1992), "Partial embedment effects on soil-structure interaction", Proceedings of the 10th World Conference on Earthquake Engineering, Madrid, Span, July.
  9. Imamura, A., Watanabe, T., Ishizaki, M. and Motosaka, M. (1992), "Seismic response characteristics of embedded structures considering cross interaction", Proceedings of the 10th World Conference on Earthquake Engineering, Madrid, Span, July.
  10. Karabalis, D.L. and Mohammadi, M. (1991), "3-D dynamic foundation-soil-foundation interaction on layered Soil", Soil Dyn. Earthq. Eng., 17, 139-152.
  11. Kausel, E. and Peek, R. (1982), "Dynamic loads in the interior of layered stratum: an explicit solution", Bull. Seismol. Soc. Am., 72(5), 1459-1481.
  12. Kausel, E. and Roesset, J.M. (1981), "Stiffness matrix for layered soil", Bull. Seismol. Soc. Am., 72, 1459-1481.
  13. Kausel, E., Whitman, R.V., Morray, J.P. and Elsabee, F. (1978), "The spring method for embedded foundations", Nucl. Eng. Des., 48, 377-392. https://doi.org/10.1016/0029-5493(78)90085-7
  14. Kazakov, K.S. (2012), "Elastodynamic infinite elements based on modified Bessel shape functions, applicable in the finite element method", Struct. Eng. Mech., 42(3), 353-362. https://doi.org/10.12989/sem.2012.42.3.353
  15. Lin, H.T. and Tassoulas, J.L. (1987), "A hybrid method for three-dimensional problems of dynamics of foundations", Earthq. Eng. Struct. Dyn., 14, 61-74.
  16. Liou, G.S. (1992), "Impedance for rigid square foundation on layered medium", Struct. Eng. Earthq. Eng., 9, 33-44.
  17. Liou, G.S. and Chung, I.L, (2009), "Impedance matrices for circular foundation embedded in layered medium", Soil Dyn. Earthq. Eng., 29, 677-692. https://doi.org/10.1016/j.soildyn.2008.07.004
  18. Luco, J.E. and Wong, H.L. (1977), "Dynamic responseof rectangular foundations for Rayleigh wave excitation", Proceedings of the 6th World Conference of Earthquake Engineering, New Delhi, India, January.
  19. Lysmer, J. and Waas, G. (1972), "Shear waves in plane infinite structures", J. Eng. Mech. Div., ASCE, 98(EM1), 85-105.
  20. Lee, J.H., Kim, J.K. and Tassoulas, J.L. (2012), "Dynamic analysis of foundations in a layered half-space using a consistent transmitting boundary", Earthq. Struct., 3(3), 203-230. https://doi.org/10.12989/eas.2012.3.3_4.203
  21. McKay, K. (2009), "Three applications of the reciprocal theorem in soil-structure interaction", Ph.D. Dissertation, University of Southern California, California.
  22. Mizuhata, K., Kusakabe, K. and Shirase, Y. (1988), "Study on dynamic characteristics of embedded mass and its surrounding ground", Proceedings of the9th World Conference on Earthquake Engineering, Tokyo-Kyoto, Japan, August.
  23. Mohammadi, M. (1992), "3-D dynamic foundation-soil-foundation interaction by BEM", Ph.D. Dissertation, University of South Carolina, Columbia.
  24. Pecker, A. (1984), Dynamique des sols, Presses de l'Ecole Nationale des Ponts et Chaussees, Paris, France.
  25. Qian, J. and Beskos, D.E. (1996), "Harmonic wave response of two 3-D rigid surface foundations", Earthq. Eng. Struct. Dyn., 15, 95-110. https://doi.org/10.1016/0267-7261(95)00026-7
  26. Sbartai, B. and Boumekik, A. (2008), "Ground vibration from rigid foundation by BEM-TLM", ISET J. Tech., 45(3-4), 67-78.
  27. Sbartai, B. (2016), "Dynamic interaction of two adjacent foundations embedded in a viscoelastic soil", Int. J. Struct. Stab. Dyn., 16(3), 1450110.
  28. Spyrakos, C.C. and Xu, C. (2004), "Dynamic analysis of flexible massive strip-foundations embedded inlayered soils by hybrid BEM-FEM", Comput. Struct., 82, 2541-2550. https://doi.org/10.1016/j.compstruc.2004.05.002
  29. Suarez, M., Aviles, J., Francisco, J. and Sanchez-Sesma, F.J. (2002), "Response of L-shaped rigid foundations embedded in a uniform half-space to travelling seismic waves", Soil Dyn. Earthq. Eng., 22, 625-637. https://doi.org/10.1016/S0267-7261(02)00058-1
  30. Watakabe, M., Matsumoto, H., Ariizumi, K., Fukahori, Y., Shikama, Y., Yamanouchi, K. and Kuniyoshi, H. (1992), "Earthquake observation of deeply embedded building structure", Proceedings of the10th World Conference on Earthquake Engineering, Madrid, Span, July.
  31. Wong, H.L. and Luco, J.E. (1986), "Dynamic interaction between rigid foundations in a layered half-space", Soil Dyn. Earthq. Eng., 5(3), 149-158. https://doi.org/10.1016/0267-7261(86)90018-7
  32. Wong, H.L. and Luco, J.E. (1978), "Dynamic response of rectangular foundations to obliquely incident seismic waves", Earthq. Eng. Struct. Dyn., 6, 3-16. https://doi.org/10.1002/eqe.4290060103

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