Earthquakes and Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Dynamic analysis of foundations in a layered half-space using a consistent transmitting boundary

  • Lee, Jin Ho (Department of Civil, Architectural and Environmental Engineering, the University of Texas at Austin) ;
  • Kim, Jae Kwan (Department of Civil and Environmental Engineering, Seoul National University) ;
  • Tassoulas, John L. (Department of Civil, Architectural and Environmental Engineering, the University of Texas at Austin)
  • Received : 2011.07.11
  • Accepted : 2011.10.31
  • Published : 2012.06.25
⟨ Previous Next ⟩

Abstract

This paper presents results for impedance (and compliance) functions and input motions of foundations in a layered half-space computed on the basis of a procedure that combines a consistent transmitting boundary with continued-fraction absorbing boundary conditions which are accurate and effective in modeling wave propagation in various unbounded domains. The effects of obliquely incident seismic waves in a layered half-space are taken into account in the formulation of the transmitting boundary. Using the numerical model, impedance (and compliance) functions and input motions of rigid circular foundations on the surface of or embedded in a homogeneous half-space are computed and compared with available published results for verification of the procedure. Extrapolation methods are proposed to improve the performance in the very-low-frequency range and for the static condition. It is concluded from the applications that accurate analysis of foundation dynamics and soil-structure interaction in a layered half-space can be carried out using the enhanced consistent transmitting boundary and the proposed extrapolations.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea

References

  1. Andrade, P.W. (1999), Implementation of second-order absorbing boundary conditions in frequency-domain computations, Ph.D. Dissertation, The University of Texas at Austin, Texas.
  2. Apsel, R.J. and Luco, J.E. (1987), "Impedance functions for foundations embedded in a layered medium: an integral equation approach", Earthq. Eng. Struct. D., 15(2), 213-231. https://doi.org/10.1002/eqe.4290150205
  3. Bougacha, S., Tassoulas, J.L. and Roesset, J.M. (1993a), "Analysis of foundations on fluid-filled poroelastic stratum", J. Eng. Mech.-ASCE, 119(8), 1632-1648. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:8(1632)
  4. Bougacha, S., Tassoulas, J.L. and Roësset, J.M. (1993b), "Dynamic stiffness of foundations on fluid-filled poroelastic stratum", J. Eng. Mech.-ASCE, 119(8), 1649-1662. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:8(1649)
  5. Day, S.M. (1977), Finite element analysis of seismic scattering problems, PhD Dissertation, Univ. of California, San Diego, La Jolla, California.
  6. Gazetas, G. and Roesset, J.M. (1976), "Forced vibrations of strip footings on layered soil", Method. Struct. Anal.- ASCE, 1, 115-131.
  7. Gazetas, G. and Roesset, J.M. (1979), "Vertical vibration of machine foundations", J. Geotech. Eng. Div.-ASCE, 105(12), 1435-1454.
  8. Gladwell, G.M.L. (1968), "Forced tangential and rotator vibration of a rigid circular disc on a semi-infinite solid", Int. J. Eng. Sci., 6(10), 591-607. https://doi.org/10.1016/0020-7225(68)90061-X
  9. Guddati, M.N. (2006), "Arbitrarily wide-angle wave equations for complex media", Comput. Method. Appl. M.. Eng., 195(1-3), 65-93. https://doi.org/10.1016/j.cma.2005.01.006
  10. Iguchi, M. (1984), "Earthquake response of embedded cylindrical foundations to SH and SV waves", Proceedings of the 8th World Conference of Earthquake Engineering, San Francisco.
  11. Kausel, E. (1974), Forced vibrations of circular foundations on layered media, Research Report R74-11, Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts.
  12. Kausel, E. (1996), "Discussion: Dynamic response of a multi-layered poroelastic medium by Rajapakse R.K.N.D and Senjuntichai, T.", Earthq. Eng. Struct. D., 25(10), 1165-1167. https://doi.org/10.1002/(SICI)1096-9845(199610)25:10<1165::AID-EQE600>3.0.CO;2-I
  13. Kausel, E., Roësset, J.M. and Waas, G. (1975), "Dynamic analysis of footings on layered media", J. Eng. Mech. Div.-ASCE, 101(5), 679-693.
  14. Kausel, E. and Roesset, J.M. (1975), "Dynamic stiffness of circular foundations", J. Eng. Mech. Div.-ASCE, 101(6), 771-785.
  15. Lee, J.H, Kim, J.K. and Tassoulas, J.L. (2011a), "Implementation of a second-order paraxial boundary condition for a water-saturated layered half-space in plane strain", Earthq. Eng. Struct. D., 40(5), 531-550. https://doi.org/10.1002/eqe.1047
  16. Lee, J.H., Kim, J.K. and Tassoulas, J.L. (2011b), "Application of a second-order paraxial boundary condition to the problems of dynamics of circular foundations on a porous layered half-space", Soil Dyn. Earthq. Eng., 31(3), 291-305. https://doi.org/10.1016/j.soildyn.2010.08.005
  17. Lee, J.H. and Tassoulas, J.L. (2011), "Consistent transmitting boundary with continued-fraction absorbing boundary conditions for analysis of soil-structure interaction in a layered half-space", Comput. Method. Appl. Mech. Eng., 200(13-16), 1509-1525. https://doi.org/10.1016/j.cma.2011.01.004
  18. Lin, H.T., Roesset, J.M. and Tassoulas, J.L. (1987), "Dynamic interaction between adjacent foundations", Earthq. Eng. Struct. D., 15(3), 323-343. https://doi.org/10.1002/eqe.4290150304
  19. Luco, J.E. (1982), "Linear soil-structure interaction: a review", in: Datta, S.K. (eds.), Earthquake ground motion and its effects on structures, AMD-vol. 53, ASME, New York, 41-57.
  20. Luco, J.E. and Mita, A. (1987), "Response of a circular foundation on a uniform half-space to elastic waves", Earthq. Eng. Struct. D., 15(1), 105-118. https://doi.org/10.1002/eqe.4290150108
  21. Luco, J.E. and Westmann, R.A. (1971), "Dynamic response of circular footings", J. Eng. Mech. Div.-ASCE, 97(5), 1381-1395.
  22. Luco, J.E. and Westmann, R.A. (1972), "Dynamic response of a rigid footing bonded to an elastic half space", J. Appl. Mech. ASME, 39, 527-541. https://doi.org/10.1115/1.3422711
  23. Luco, J.E. and Wong, H.L. (1987), "Seismic response of foundations embedded in a layered half-space", Earthq. Eng. Struct. D., 15(2), 233-247. https://doi.org/10.1002/eqe.4290150206
  24. Pais, A.L. and Kausel, E. (1989), "On rigid foundations subjected to seismic waves", Earthq. Eng. Struct. D., 18(4), 475-489. https://doi.org/10.1002/eqe.4290180403
  25. Robertson, I.A. (1966), "Forced vertical vibration of a rigid circular disc on a semi-infinite elastic solid", Proc. Camb. Phil. Soc., 62(3), 547-553. https://doi.org/10.1017/S0305004100040184
  26. Roesset, J.M. (1980), "A review of soil-structure interaction", Report UCRL-15262, Seismic Safety Margins Research Program, Lawrence Livermore Laboratory.
  27. Tassoulas, J.L. (1981), Elements for the numerical analysis of wave motion in layered media, Research Report R81-2, Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts.
  28. Tassoulas, J.L. (1984), "An investigation of the effect of the rigid sidewall on the response of embedded circular foundations to obliquely incident SV- and P-waves", Int. Symp. Dyn. Soil Struct. Interact., Minneapolis, 4-5 September, 55-64.
  29. Thomas, D.P. (1968), "A note on the torsional oscillations of an elastic half space", Int. J. Eng. Sci., 6(10), 565- 570. https://doi.org/10.1016/0020-7225(68)90058-X
  30. Waas, G. (1972), Linear two-dimensional analysis of soil dynamics problems in semi-infinite layered media, Ph.D. Dissertation, University of California, Berkeley, California.
  31. Wong, H.L. (1975), Dynamic soil-structure interaction, Report EERL-75-01, Earthquake Engineering Research Laboratory, California Institute of Technology, Pasadena, California.
  32. Wong, H.L. and Luco, J.E. (1978a), Tables of impedance functions and input motions for rectangular foundations, Report CE 78-15, Department of Civil Engineering, University of Southern California, Los Angeles, California.
  33. Wong, H.L. and Luco, J.E. (1978b), "Dynamic response of rectangular foundations to obliquely incident seismic waves", Earthq. Eng. Struct. D., 6(1), 3-16. https://doi.org/10.1002/eqe.4290060103

Cited by

  1. Characteristics of Earthquake Responses of an Isolated Containment Building in Nuclear Power Plants According to Natural Frequency of Soil vol.17, pp.6, 2013, https://doi.org/10.5000/EESK.2013.17.6.245
  2. Dynamic analysis of a layered half-space subjected to moving line loads vol.47, 2013, https://doi.org/10.1016/j.soildyn.2012.07.013
  3. Seismic response of a rigid foundation embedded in a viscoelastic soil by taking into account the soil-foundation interaction vol.58, pp.5, 2016, https://doi.org/10.12989/sem.2016.58.5.887
  4. Nonlinear analysis of soil–structure interaction using perfectly matched discrete layers vol.142, 2014, https://doi.org/10.1016/j.compstruc.2014.06.002
  5. Pseudo 3D FEM analysis for wave passage effect on the response spectrum of a building built on soft soil layer vol.8, pp.5, 2015, https://doi.org/10.12989/eas.2015.8.5.1241
  6. Dynamic analysis of a poroelastic layered half-space using continued-fraction absorbing boundary conditions vol.263, 2013, https://doi.org/10.1016/j.cma.2013.05.002
  7. Dynamic Response of Arbitrarily Shaped Foundation Embedded in Multilayered Partially Saturated Half-Space vol.19, pp.11, 2012, https://doi.org/10.1061/(asce)gm.1943-5622.0001501