Earthquakes and Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Harmonic seismic waves response of 3D rigid surface foundation on layer soil

  • Messioud, Salah (LGCE, University of Jijel) ;
  • Sbartai, Badredine (Department of Civil Engineering, University of Badji Mokhtar-Annaba) ;
  • Dias, Daniel (School of Automotive and Transportation Engineering, Hefei University of Technology)
  • Received : 2017.09.11
  • Accepted : 2018.12.15
  • Published : 2019.01.25
⟨ Previous Next ⟩

Abstract

This study, analyses the seismic response for a rigid massless square foundation resting on a viscoelastic soil layer limited by rigid bedrock. The foundation is subjected either to externally applied forces or to obliquely incident seismic body or surface harmonic seismic waves P, SV and SH. A 3-D frequency domain BEM formulation in conjunction with the thin layer method (TLM) is adapted here for the solution of elastodynamic problems and used for obtained the seismic response. The mathematical approach is based on the method of integral equations in the frequency domain using the formalism of Green's functions (Kausel and Peck 1982) for layered soil, the impedance functions are calculated by the compatibility condition. In this study, The key step is the characterization of the soil-foundation interaction with the input motion matrix. For each frequency the impedance matrix connects the applied forces to the resulting displacement, and the input motion matrix connects the displacement vector of the foundation to amplitudes of the free field motion. This approach has been applied to analyze the effect of soil-structure interaction on the seismic response of the foundation resting on a viscoelastic soil layer limited by rigid bedrock.

Keywords

References

  1. Ahmad, S. and Rupani, A.K. (1999), "Horizontal impedance of square foundation in layered soil", Soil Dyn. Earthq. Eng., 18(1), 59-69. https://doi.org/10.1016/S0267-7261(98)00028-1
  2. Akino, K., Ohtsuka, Y., Fukuoka, A. and Ishida, K. (1996), "Experimental studies on embedment effects on dynamic soil-structure interaction", 11th World Conference on Earthquake Engineering, Paper No. 59.
  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. Aubry, D. and Clouteau, D. (1992), "A subdomain approach to dynamic soil-structure interaction", Earthq. Eng. Struct. Dyn., 251-272. https://doi.org/10.1002/(SICI)1096-9845(199702)26:2<251::AID-EQE642>3.0.CO;2-B
  5. Auersch, L. (2013), "Response to harmonic wave excitation of finite or infinite elastic plates on a homogeneous or layered half-space", Comput. Geotech., 51, 50-59. https://doi.org/10.1016/j.compgeo.2013.02.001
  6. Beskos, D.E. (1987), "Boundary element methods in dynamic analysis", Appl. Mech. Rev., 40, 1-23. https://doi.org/10.1115/1.3149529
  7. Cai, Y and Hu, X. (2010), "Vertical vibrations of a rigid foundation embedded in a poroelastic half space", J. Eng. Mech., 136(3), 390-398. https://doi.org/10.1061/(ASCE)0733-9399(2010)136:3(390)
  8. Cao, Y.M., Xia, H. and Lombaert, G. (2010), "Solution of moving-load-induced soil vibrations based on the Betti-Rayleigh Dynamic Reciprocal Theorem", Soil Dyn. Earthq. Eng., 30(6), 470-480. https://doi.org/10.1016/j.soildyn.2010.01.003
  9. 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
  10. Chung, I.L. and Liou, G.S. (2013), "Calculation of impedances for axial symmetric foundation embedded in half-space medium using solutions for one layer stratum", Lat. Am. J. Solid. Struct., 10(6), 1225-1241. https://doi.org/10.1590/S1679-78252013000600008
  11. Fujimori, T., Tsundoa, T., Izumi, M. and Akino, K. (1992), "Partial embedment effects on soil-structure interaction", 10th World Conference on Earthquake Engineering, 3, 1713-1718.
  12. Gazetas, G. (1980), "Static and dynamic displacements of foundations on heterogeneous multilayered soils", Geotechnique, 30(2), 159-177. https://doi.org/10.1680/geot.1980.30.2.159
  13. Karabalis, D.L. and Mohammadi, M. (1991), "3-D dynamic foundation-soil-foundation interaction on layered Soil", Soil Dyn. Earthq. Eng., 17, 139-152. https://doi.org/10.1016/S0267-7261(97)00047-X
  14. 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. https://doi.org/10.1785/BSSA0720051459
  15. Kausel, E. and Roesset, J.M. (1981), "Stiffness matrix for layered soil", Bull. Seismol. Soc. Am., 72, 1459-1481. https://doi.org/10.1785/BSSA0720051459
  16. 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
  17. Kumar, A., Manna, B. and Rao, K.S. (2013), "Dynamic response of block foundations resting on soil-rock and rock-rock system under vertical excitation", Ind. Geotech. J., 43(1), 83-95. https://doi.org/10.1007/s40098-012-0036-0
  18. Lin, H.T. and Tassoulas, J.L. (1987), "A hybrid method for threedimensional problems of dynamics of foundations", Earthq. Eng. Struct. Dyn., 14, 61-74. https://doi.org/10.1002/eqe.4290140105
  19. Liou, G.S. (1989), "Analytic solutions for soil-structure interaction in layered media", Earthq. Eng. Struct. Dyn., 18(5), 667-686. https://doi.org/10.1002/eqe.4290180507
  20. Liou, G.S. (2013), "Vibrations induced by harmonic loadings applied at circular plate on layered medium", J. Mech., 29(2), 197-206. https://doi.org/10.1017/jmech.2012.137
  21. Liou, G.S. and Chung, I.L. (2009), "Impedance matrices for circular foundation embedded in layered medium", Soil Dyn. Earthq. Eng., 29(4), 677-692. https://doi.org/10.1016/j.soildyn.2008.07.004
  22. Luco, J.E. and Wong, H.L. (1977), "Dynamic response of rectangular foundations for Rayleigh wave excitation", 6th World Conference of Earthquake Engineering, New Delhi, India.
  23. Lysmer, J. and Waas, G. (1972), "Shear waves in plane infinite structures", J. Eng. Mech. Div., ASCE, 98(1), 85-105. https://doi.org/10.1061/JMCEA3.0001583
  24. Mandal, A. and Baidya, D.K. (2004), "Effect of presence of rigid base within the soil on the dynamic response of rigid surface foundation", Geotech. Test. J., 27(5), 475-482.
  25. Mandal, A., Baidya, D.K. and Roy, D. (2012), "Dynamic response of the foundations resting on a two-layered soil underlain by a rigid layer", Geotech. Geolog. Eng., 30(4), 775-786. https://doi.org/10.1007/s10706-012-9497-2
  26. McKay, K. (2009), "Three applications of the reciprocal theorem in soil-structure interaction", Ph.D. Thesis, University of Southern California.
  27. Messioud, S., Sbartai, B. and Dias, D. (2016), "Seismic response of a rigid foundation embedded in a viscoelastic soil by taking into account the soil-foundation interaction", Struct. Eng. Mech., 58(5), 887-903. https://doi.org/10.12989/sem.2016.58.5.887
  28. Mizuhata, K., Kusakabe, K. and Shirase, Y. (1988), "Study on dynamic characteristics of embedded mass and its surrounding ground", 9th World Conference on Earthquake Engineering, 3, 679-685.
  29. Mohammadi, M. (1992), "3-D dynamic foundation-soil-foundation interaction by BEM", Ph.D. Thesis, University of South Carolina, Columbia.
  30. Pecker, A. (1984) Dynamique Des Sols, Presses de l'Ecole Nationale des Ponts et Chaussees.
  31. 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
  32. Sbartai, B. and Boumekik, A. (2008), "Ground vibration from rigid foundation by BEM-TLM", ISET J. Technol., 45(3-4), 6778.
  33. 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
  34. Watakabe, M., Matsumoto, H., Ariizumi, K., Fukahori, Y., Shikama, Y., Yamanouchi, K. and Kuniyoshi, H. (1992), "Earthquake observation of deeply embedded building structure", 10th World Conference on Earthquake Engineering, 3, 1831-1833.
  35. 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
  36. 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

Cited by

  1. A polynomial mathematical tool for foundation-soil-foundation interaction vol.23, pp.6, 2019, https://doi.org/10.12989/gae.2020.23.6.547