Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Efficient analysis of SSI problems using infinite elements and wavelet theory

  • Received : 2010.07.18
  • Accepted : 2010.10.20
  • Published : 2010.12.25
⟨ Previous Next ⟩

Abstract

In this paper, Soil-Structure Interaction (SSI) effect is investigated using a new and integrated approach. Faster solution of time dependant differential equation of motion is achieved using numerical representation of wavelet theory while dynamic Infinite Elements (IFE) concept is utilized to effectively model the unbounded soil domain. Combination of the wavelet theory with IFE concept lead to a robust, efficient and integrated technique for the solution of complex problems. A direct method for soil-structure interaction analysis in a two dimensional medium is also presented in time domain using the frequency dependent transformation matrix. This matrix which represents the far field region is constructed by assembling stiffness matrices of the frequency dependant infinite elements. It maps the problem into the time domain where the equations of motion are to be solved. Accuracy of results obtained in this study is compared to those obtained by other SSI analysis techniques. It is shown that the solution procedure discussed in this paper is reliable, efficient and less time consuming as compared to other existing concepts and procedures.

Keywords

References

  1. ANSYS 5.4 (1997), Basic analysis procedures guide, 000856, 2nd Edition, SASIP, Inc.
  2. Bagheripour, M.H. and Marandi, S.M. (2003), "Analysis of static and dynamic problems in geotechnics with infinite elements", Proceedings of Sixth International Conference in Civil Engineering, Isfahan University of Technology, Iran.
  3. Bagheripour, M.H. and Marandi, S.M. (2005), "A numerical model for unbounded soil domain in earthquake SSI analysis using periodic infinite elements", Int. J. Civil Eng., 3(2), 96-111.
  4. Baziar Mansour Khani, M.H. (2007), "Dynamic soil-structure interaction analysis using the scaled boundary element method", PhD thesis, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, Australia.
  5. Boore, D. (2008), "TSPP, A collection of FORTRAN programs for processing and manipulating time series", U.S Geological Survey Open-File Report 2008-1111, Version 1.2, March.
  6. Bettes, P. (1977), "Infinite elements", Int. J. Numer. Meth. Eng., 11, 355-375. https://doi.org/10.1002/nme.1620110210
  7. Brinkgreve, R.B.J., Vermeer, P.A. and Bakker, K.J. (1988), Material model manual, PLAXIS V.7, A.A. Balkema, Rotterdam, Brookfield.
  8. Cattani, C. (2004), "Haar wavelet based on technique in evolution problems", Proc. Estonian Academic Sci. Phys. Math., 51, 45-63.
  9. Chen, C.F. and Hesiao, C.H. (1997), "Haar wavelet method for solving lumped and distributed-parameter systems", IEE P. - Contr. Theor. Ap., 144, 87-94. https://doi.org/10.1049/ip-cta:19970702
  10. Chen, C.F. and Hesiao, C.H. (1997), "Wavelet approach to optimizing dynamic systems", IEE P. - Contr. Theor. Ap., 144, 213-219.
  11. Chore, H.S., Ingle, R.K. and Sawant, V.A. (2009), "Building frame-pile foundation-soil interactive analysis", Interact. Multiscale Mech., 2(4), 397-411. https://doi.org/10.12989/imm.2009.2.4.397
  12. Chow, Y.K., and Smith, I.M. (1981), "Static and periodic infinite solid elements", Int. J. Numer. Math. Eng., 17, 503-526. https://doi.org/10.1002/nme.1620170403
  13. Chuhan, Z. and Zhao, C. (1987), "Coupling method of finite and infinite elements for strip foundation wave problems", Earthq. Eng. Struct. Dyn., 15, 839-85. https://doi.org/10.1002/eqe.4290150705
  14. Cundall, P.A., Kunar, R.R., Carpenter, P.C. and Marti, J. (1978), "Solution of infinite dynamic problems by finite modeling in the time domain", Conference on Applied Numerical Modelling, Madrid.
  15. Darbre, G.R. and Wolf, J.P. (1988), "Criterion of stability and implementation issues of hybrid frequency-time domain procedure for non-linear dynamic analysis", Earthq. Eng. Struct. Dyn., 16, 569-581. https://doi.org/10.1002/eqe.4290160408
  16. Deneme, I.O., Yerli, H.R., Severcan, M.H., Tanrikulu, A.H. and Tanrikulu, A.K. (2009), "Use and comparison of different types of boundary elements for 2D soil-structure interaction problems", Adv. Eng. Softw., 40, 847- 855. https://doi.org/10.1016/j.advengsoft.2009.01.006
  17. Ding, H.P. and Liao, Z.P. (2001), "A hybrid analysis method for linear dynamic soil-structure interaction in time and frequency domain", ACTA Seismol. Sinica, 14 (4), 440-447. https://doi.org/10.1007/s11589-001-0122-3
  18. Goedecker, S. and Ivanov, O. (1998), "Solution of multi scale partial differential equations using wavelets", Comput. Phys., 12(6), 548-555. https://doi.org/10.1063/1.168739
  19. Gouasmia, A. and Djeghaba, K. (2007), "Non-linear seismic soil-structure interaction analysis of structures based the substructure method", Asian J. Civil Eng. (Bulid. Housing), 8(2), 183-201.
  20. Heidari, A. (2004), "Optimum design of structures against earthquake by advanced optimization methods", PhD thesis, University of Kerman, Iran.
  21. Hsiao, C.H. and Wang, W.J. (2001), "Haar wavelet approach to nonlinear stiff systems", Math. Comput. Simulat., 57, 347-353. https://doi.org/10.1016/S0378-4754(01)00275-0
  22. Kausel, E. (1974), "Forced vibration of circular foundations in layered media", MIT Research Report R74-11, MIT.
  23. Kausel, E. (2010), "Early history of soil-structure interaction", J. Soil Dyn. Earthq. Eng., 30, 822-832. https://doi.org/10.1016/j.soildyn.2009.11.001
  24. Kim, D.K. (1999), "Analytical frequency-dependent infinite elements for soil-structure interaction analysis in time domain", PhD Dissertation, Korea Advanced Institute of Science and Technology, Korea.
  25. Kim, D.K. and Yun, C. (2000), "Time domain soil structure interaction analysis in two-dimensional medium based on analytical frequency dependant infinite elements", Int. J. Numer. Meth. Eng., 47, 1241-1261. https://doi.org/10.1002/(SICI)1097-0207(20000310)47:7<1241::AID-NME807>3.0.CO;2-9
  26. Kramer, S. L. (1996), Geotechnical earthquake engineering, Prentice Hall, N.J.
  27. Lepik, U. (2004), "Numerical solution of differential equations using haar wavelets", Math. Comput. Simulat.
  28. Liao, Z.P., Wong, H.L. and Yifan, Y. (1984), "A transmitting boundary for transient wave analysis", J. Eng. Mech. Division - ASCE, 27, 1063-1073.
  29. Logan, D. L. (2008), A first course in the finite element method, 4th Edition, Thompson.
  30. Lysmer, J. and Kuhlemeyer, R.L. (1969), "Finite dynamic model for infinite media", J. Eng. Mech. Division - ASCE, 95, 850-877.
  31. Masia, M.J., Kleeman, P.W. and Melchers, R.E. (2004), "Modeling soil-structure interaction for masonry structures", J. Struct. Eng. - ASCE, 130(4), 641-649. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:4(641)
  32. Matlab R2009B, Version 7.9.0.529, Mathworks Inc., USA.
  33. Nakhaei, M. and Ghannad, M.A. (2006), "The effect of soil-structure interaction on hysteretic energy demand of buildings", Struct. Eng. Mech., 24(5), 641-645. https://doi.org/10.12989/sem.2006.24.5.641
  34. Riddell, R. and Garcia, J.E. (2001), "Hysteretic energy spectrum and damage control", Earthq. Eng. Struct. Dyn., 30, 1791-1816. https://doi.org/10.1002/eqe.93
  35. Tabatabaiefar, H.R. and Massumi, A. (2010), "A simplified method to determine seismic responses of reinforced concrete moment resisting building frames under influence of soil-structure interaction", J. Soil Dyn. Earthq. Eng. (in press)
  36. Wang, J. (2005), "Influence of different boundary conditions on analysis of SSI", Proceedings of 18th International Conference on Structural Mechanics in Reactor Technology (SMIRT 18), Beijing China, August 7-12.
  37. White, W., Valliappan, S. and Lee, I.K. (1977), "Unified boundary for finite dynamic models", J. Eng. Mech. Division - ASCE, 103, 949-964.
  38. Wolf, J.P. (1985), Dynamic soil structure interaction, Prentice Hall, Englewood Cliffs, N.J.
  39. Wolf, J.P. (1994), Foundation vibration analysis using simple physical models, Prentice-Hall, Englewood Cliffs, NJ.
  40. Yun, C.B., Kim, D.K. and Kim, J.M. (2000), "Analytical frequency-dependent infinite elements for soil-structure interaction analysis in two dimensional medium", Eng. Struct., 22, 258-271. https://doi.org/10.1016/S0141-0296(98)00070-4
  41. Zhao, C., Valliappan, S. and Wang, Y.C. (1991), "An approximate method for simulating infinite media", Comput. Struct., 41(5), 1041-1049. https://doi.org/10.1016/0045-7949(91)90298-Z
  42. Zhao, C. and Valliappan, S.A. (1992), "Dynamic infinite element for 3-D infinite domain wave problems", Int. J. Numer. Math. Eng., 36, 2567-2580.
  43. Zhao, C. and Zhang, C. (1989), "Analysis of 3-D foundation wave problems by mapped dynamic infinite elements", J. Sci. China, 32(4), 479-491.

Cited by

  1. Optimization of ground response analysis using wavelet-based transfer function technique vol.7, pp.2, 2014, https://doi.org/10.12989/gae.2014.7.2.149
  2. Ground response analysis using non-recursive matrix implementation of hybrid frequency-time domain (HFTD) approach vol.18, pp.6, 2011, https://doi.org/10.1016/j.scient.2011.11.019
  3. Centrifuge modelling of temporary roadway systems subject to rolling type loading vol.3, pp.1, 2010, https://doi.org/10.12989/gae.2011.3.1.045
  4. Synchrosqueezed wavelet transform for frequency and damping identification from noisy signals vol.9, pp.5, 2012, https://doi.org/10.12989/sss.2012.9.5.441
  5. Earthquake time-frequency analysis using a new compatible wavelet function family vol.3, pp.6, 2010, https://doi.org/10.12989/eas.2012.3.6.839
  6. Zemin-yapı etkileşiminin betonarme bacaların dinamik davranışına etkisi vol.7, pp.1, 2010, https://doi.org/10.29130/dubited.465732
  7. Seismic performance of outrigger-belt truss system considering soil-structure interaction vol.11, pp.1, 2010, https://doi.org/10.1007/s40091-019-0215-7