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Forced vibration of surface foundation on multi-layered half space

  • Chen, Lin (Lehrstuhl fur Baustatik und Baudynamik, RWTH Aachen University)
  • 투고 : 2014.04.02
  • 심사 : 2014.11.06
  • 발행 : 2015.05.25

초록

A numerical approach is presented for the analysis of the forced vibration of a rigid surface foundation with arbitrary shape. In the analysis, the foundation is discretized into a number of sub squaree-lements. The dynamic response within each sub-element is described by the Green's function, which is obtained by the Fourier-Bessel transform and Precise Integration Method (PIM). Incorporating the displacement boundary condition and force equilibrium of the foundation, it obtains a system of linear algebraic equation in terms of the contact forces within each sub-element. Solving the equation leads to the desired dynamic impedance functions of the foundation. Numerical results are obtained for foundation not only with simple geometrical configurations, such as rectangular and circular foundation, but also the case of irregularly shaped foundation. Several comparisons between the proposed approach and other methods are made. Very good agreement is reached. Also, parametric studies are carried out on the dynamic response of foundation. Addressed in this study are the effects of Poisson's ratio, material damping and contact condition of soil-foundation interface. Several conclusions are drawn the significance of the factors.

키워드

참고문헌

  1. Abascal, R. and Dominguez, J. (1986), "Vibrations of footings on zoned viscoelastic soils", J. Eng. Mech., 112(5), 433-447. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:5(433)
  2. Alarcon, E., Cano, J.J. and Dominguez, J. (1989), "Boundary element approach to the dynamic stiffness functions of circular foundation", Int. J. Numer. Anal. Methods Geomech, 13(6), 645-664. https://doi.org/10.1002/nag.1610130606
  3. Chave, A.D. (1983), "Numerical integration of related Hankel transforms by quadrature and continued fraction expansion", Geophys., 48(12), 1671-1686. https://doi.org/10.1190/1.1441448
  4. Dominguez, J. and Roesset, J. (1978), "Dynamic stiffness of rectangular foundation", NASA STI/Recon Technical Report N 79, 16152.
  5. Ellis, E. and Springman, S. (2001), "Modelling of soil-structure interaction for a piled bridge abutment in plane strain FEM analyses", Comput. Geotech., 28(2), 79-98. https://doi.org/10.1016/S0266-352X(00)00025-2
  6. Estorff, V.O. and Firuziaan, M. (2000), "Coupled BEM/FEM approach for nonlinear soil/structure interaction", Eng. Anal. Bound. Elem., 24(10), 715-725. https://doi.org/10.1016/S0955-7997(00)00054-0
  7. Galvin, P., Romero, A. and Dominguez, J. (2010), "Fully three-dimensional analysis of high-speed train- track-soil-structure dynamic interaction", J. Sound Vib., 329(24), 5147-5163. https://doi.org/10.1016/j.jsv.2010.06.016
  8. Gao, Q., Lin, J.H., Zhong, W.X., Howson, W.P., Williams, F.W. (2006), "A precise numerical method for Rayleigh waves in a stratified half space", Int. J. Numer. Meth. Eng., 67(6), 771-786. https://doi.org/10.1002/nme.1644
  9. Gazetas, G. (1980), "Static and dynamic displacements of foundation on heterogeneous multilayered soils", Geotech., 30(2), 159-177. https://doi.org/10.1680/geot.1980.30.2.159
  10. Gazetas, G. (1981), "Strip foundation on a cross-anisotropic soil layer subjected to dynamic loading", Geotech., 31(2), 161-179. https://doi.org/10.1680/geot.1981.31.2.161
  11. Jeremic, B., Jie, G., Preisig, M. and Tafazzoli, N. (2009), "Time domain simulation of soil-foundationstructure interaction in non-uniform soils", Earthq. Eng. Struct. Dyn., 38(5), 699-718. https://doi.org/10.1002/eqe.896
  12. Ju, S.H., Ho, Y.S. and Leong, C.C. (2012), "A finite element method for analysis of vibration induced by maglev trains", J. Sound Vib., 331(16), 3751-3761. https://doi.org/10.1016/j.jsv.2012.04.004
  13. Karabalis, D. and Beskos, D. (2006), "Dynamic response of 3-D rigid surface foundation by time domain boundary element method", Earthq. Eng. Struct. Dyn., 12(1), 73-93. https://doi.org/10.1002/eqe.4290120106
  14. Karabalis, D.L. and Beskos, D.E. (1985), "Dynamic response of 3-D flexible foundation by time domain BEM and FEM", Int. J. Soil Dyn. Earthq. Eng., 4(2), 91-101. https://doi.org/10.1016/0261-7277(85)90004-X
  15. Kausel, E. (1981), "An explicit solution for the Green's function for dynamic loads in layered media", NASA STI/Recon Technical Report N 82, 29505.
  16. Kausel, E. (2006), Fundamental Solutions in Elastodynamics, Cambridge University Press, Cambridge.
  17. Kausel, E. and Manolis, G.G.D. (2000), Wave Motion Problems in Earthquake Engineering, Wit Press.
  18. Kausel, E. and Roesset, J.M. (1975), "Dynamic stiffness of circular foundation", J. Eng. Mech. Div., 101(6), 771-785.
  19. Kazakov, K.S. (2010), "Elastodynamic infinite elements with united shape functions for soil-structure interaction", Finite Elem. Anal. Des., 46(10), 936-942. https://doi.org/10.1016/j.finel.2010.06.008
  20. Kim, D.K. and Yun, C.B. (2003), "Time domain earthquake response analysis method for 2-D soil-structure interaction systems", Struct. Eng. Mech., 15(6), 717-733. https://doi.org/10.12989/sem.2003.15.6.717
  21. 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. Meth. Appl. Mech. Eng., 200(13), 1509-1525. https://doi.org/10.1016/j.cma.2011.01.004
  22. Lehmann, L. (2005), "An effective finite element approach for soil-structure analysis in the timedomain", Struct. Eng. Mech., 21(4), 437-450. https://doi.org/10.12989/sem.2005.21.4.437
  23. Lin, G., Han, Z. and Li, J. (2013a), "An efficient approach for dynamic impedance of surface footing on layered half-space", Soil Dyn. Earthq. Eng., 49, 39-51. https://doi.org/10.1016/j.soildyn.2013.01.008
  24. Lin, G., Han, Z., Zhong, H. and Li, J. (2013b), "A precise integration approach for dynamic impedance of rigid strip footing on arbitrary anisotropic layered half-space", Soil Dyn. Earthq. Eng., 49, 96-108. https://doi.org/10.1016/j.soildyn.2013.01.009
  25. Lin, G., Han, Z. and Li, J. (2014), "Soil-structure interaction analysis on anisotropic stratified medium", Geotech., 64(7), 570-580. https://doi.org/10.1680/geot.14.P.043
  26. Lucas, S. (1995), "Evaluating infinite integrals involving products of Bessel functions of arbitrary order", J. Comput. Appl. Math., 64(3), 269-282. https://doi.org/10.1016/0377-0427(95)00143-3
  27. Luco, J. and Mita, A. (1987), "Response of a circular foundation on a uniform half-space to elastic waves", Earthq. Eng. Struct. Dyn., 15(1), 105-118. https://doi.org/10.1002/eqe.4290150108
  28. Luco, J.E. (1975), "Impedance functions for a rigid foundation on a layered medium", Nucl. Eng. Des., 31(2), 204-217. https://doi.org/10.1016/0029-5493(75)90142-9
  29. Luco, J.E. and Westmann, R.A. (1971), "Dynamic response of circular footings", J. Eng. Mech. Div., 97(5), 1381-1395.
  30. Reissner, E. and Sagoci, H. (1944), "Forced torsional oscillations of an elastic half-space. I", J. Appl. Phys., 15(9), 652-654. https://doi.org/10.1063/1.1707489
  31. Rizos, D. and Wang, Z. (2002), "Coupled BEM-FEM solutions for direct time domain soil-structure interaction analysis", Eng. Anal. Bound. Elem., 26(10), 877-888. https://doi.org/10.1016/S0955-7997(02)00057-7
  32. Romero, A., Galvin, P. and Dominguez, J. (2013), "3D non-linear time domain FEM-BEM approach to soil-structure interaction problems", Eng. Anal. Bound. Elem., 37(3), 501-512. https://doi.org/10.1016/j.enganabound.2013.01.001
  33. Sagoci, H. (1944), "Forced torsional oscillations of an elastic half-space. II", J. Appl. Phys., 15(9), 655-662. https://doi.org/10.1063/1.1707490
  34. Said, I., De Gennaro, V. and Frank, R. (2009), "Axisymmetric finite element analysis of pile loading tests", Comput. Geotech., 36(1), 6-19. https://doi.org/10.1016/j.compgeo.2008.02.011
  35. Sheng, X., Jones, C.J.C. and Thompson, D.J. (2006), "Prediction of ground vibration from trains using the wavenumber finite and boundary element methods", J. Sound Vib., 293(3), 575-586. https://doi.org/10.1016/j.jsv.2005.08.040
  36. Spyrakos, C. and Beskos, D. (1986), "Dynamic response of rigid strip foundation by a time domain boundary element method", Int. J. Numer. Meth. Eng., 23(8), 1547-1565. https://doi.org/10.1002/nme.1620230810
  37. Veletsos, A.S. and Verbic, B. (1973), "Vibration of viscoelastic foundation", Earthq. Eng. Struct. Dyn., 2(1), 87-102. https://doi.org/10.1002/eqe.4290020108
  38. Veletsos, A.S. and Wei, Y.T. (1971), "Lateral and rocking vibration of footings", J. Soil Mech. Found. Div., 97(9), 1227-1248
  39. Wolf, J.P. (1985), Dynamic Soil-Structure Interaction, Prentice-Hall.
  40. Wolf, J.P. and Preisig, M. (2003), "Dynamic stiffness of foundation embedded in layered halfspace based on wave propagation in cones", Earthq. Eng. Struct. Dyn., 32(7), 1075-1098. https://doi.org/10.1002/eqe.263
  41. Wong, H. and Luco, J.E. (1985), "Tables of impedance functions for square foundation on layered media", Int. J. Soil Dyn. Earthq. Eng., 4(2), 64-81. https://doi.org/10.1016/0261-7277(85)90002-6
  42. Yalcin, O.F. and Mengi, Y. (2013), "A new boundary element formulation for wave load analysis", Comput. Mech., 52(4), 815-826. https://doi.org/10.1007/s00466-013-0846-7
  43. Zhang, J., Gao, Q., Tan, S.J. and Zhong, W.X. (2012), "A precise integration method for solving coupled vehicle-track dynamics with nonlinear wheel-rail contact", J. Sound Vib., 331(21), 4763-4773. https://doi.org/10.1016/j.jsv.2012.05.033
  44. Zhong, W.X. (2004), "On precise integration method", J. Comput. Appl. Math., 163(1), 59-78. https://doi.org/10.1016/j.cam.2003.08.053
  45. Zhong, W.X. (2001), "Combined method for the solution of asymmetric Riccati differential equations", Comput. Meth. Appl. Mech. Eng., 191(1), 93-102. https://doi.org/10.1016/S0045-7825(01)00246-8

피인용 문헌

  1. Forced Vibration of Surface Foundation on Viscoelastic Isotropic Multi-Layered Stratum vol.16, pp.09, 2016, https://doi.org/10.1142/S0219455415500613
  2. Three-dimensional Green’s function for an anisotropic multi-layered half-space vol.56, pp.5, 2015, https://doi.org/10.1007/s00466-015-1203-9
  3. Elastic solutions due to a time-harmonic point load in isotropic multi-layered media vol.57, pp.2, 2016, https://doi.org/10.12989/sem.2016.57.2.327
  4. Forced vibration response in nanocomposite cylindrical shells - Based on strain gradient beam theory vol.28, pp.3, 2015, https://doi.org/10.12989/scs.2018.28.3.381