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Three-Dimensional Soil-Structure Interaction by Boundary Element Methods

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Part of the book series: Topics in Boundary Element Research ((TBOU,volume 4))

Abstract

The application of the Boundary Element Method to the linear three-dimensional soil-structure interaction problem is discussed. Detailed formulations for rigid, surface, massless foundations of arbitrary shape are given in both frequency and time domains. In both cases the foundations are assumed to rest on a linear elastic, homogeneous, and isotropic half-space and are subjected to either externally applied loads or obliquely incident body or surface waves. Results obtained by the above approaches as well as by other well established techniques are given in a comparison study. More general problems involving massive foundations and superstructures are also presented in the general framework of a substructure formulation.

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References

  1. Reissner, E., “Stationäre, axialsymmetrische, durch eine schüttelnde Masse erregte Schwingungen eines homogenen elastischen Halbraumes”, Ing. Arch., 7, 381–396 (1936).

    Article  MATH  Google Scholar 

  2. Reissner, E., “Freie und erzwungene Torsionschwingungen des elastischen Halbraumes”, Ing. Arch., 8,229–245 (1937).

    Article  MATH  Google Scholar 

  3. Richart, F.E., Jr., Hall, J.R., Jr. and Woods, R.D., “Vibrations of soils and foundations”, Prentice Hall, Englewood Cliffs, N.J., 1970.

    Google Scholar 

  4. Gazetas, G., “Analysis of machine foundation vibrations: state of the art”, Soil Dyn. Earth. Engng., 2, 2–42 (1983).

    Google Scholar 

  5. Karabalis, D.L., “Dynamic response of three-dimensional foundations”, Ph.D. Thesis, University of Minnesota, Minnespolis, Minnesota, 1984.

    Google Scholar 

  6. Seed, H.B., Whitman, R.V. and Lysmer, J., “Soil-structure interaction effects in the design of nuclear power plants”, pp. 220–241 in Hall, W.J., Ed., “Structural and Geotechnical Mechanics”, Prentice Hall, Englewood Cliffs, N.J., 1977.

    Google Scholar 

  7. Novak, M., “Foundation and soil-structure interaction”, pp. 1421–1448, in Proc. 6th World Conf. Earth. Engng., N. Delhi, India, 1977.

    Google Scholar 

  8. Luco, J.E., “Linear soil-structure interaction: a review”, pp. 41–57 in Datta, Ed., “Transient motions in earthquake engineering”, ASME, 1982.

    Google Scholar 

  9. Collins, W.D., “The forced torsional oscillations of an elastic half-space and an elastic stratum”, Proc. London Math. Soc, 12, 226–244 (1962).

    Article  MATH  MathSciNet  Google Scholar 

  10. Robertson, I.A., “Forced vertical vibration of a rigid circular disc on a semi-infinite elastic solid”, Proc. Campr. Phil. Soc., 62, 547–553 (1966).

    Article  MATH  Google Scholar 

  11. Gladwell, G.M.L., “Forced tangential and rotatory vibration of a rigid circular disc on a semi-infinite solid”, Int. J. Engng. Sci., 6, 591–607 (1968).

    Article  MATH  Google Scholar 

  12. Veletsos, A.S. and Verbic, B., “Vibration of viscoelastic foundations”, Earth. Engng. Struct. Dyn., 2, 87–102 (1973).

    Article  Google Scholar 

  13. Veletsos, A.S. and Wei, Y.T., “Lateral and rocking vibration of footings”, Proc. ASCE, 97, SM9, 1227–1248 (1971).

    Google Scholar 

  14. Luco, J.E. and Westmann, R.A., “Dynamic response of circular footings”, Proc. ASCE, 97, EM5, 1381–1395 (1971).

    Google Scholar 

  15. Luco, J.E. and Westmann, R.A., “Dynamic response of a rigid footing bonded to an elastic half- space”, J. Appl. Mech, 39, 527–534 (1972).

    Article  Google Scholar 

  16. Lamb, H., “On the propagation of tremors over the surface of an elastic solid”, Phil. Trans. Roy. Soc., London, A203, 1–42 (1904)

    Google Scholar 

  17. Lysmer, J., “Vertical motion of rigid footings”, Ph.D. dissertation, Univ. of Michigan, Ann Arbor, Michigan, August 1965.

    Google Scholar 

  18. Elorduy, J., Nieto, J.A. and Szekely, E.M., “Dynamic response of bases of arbitrary shape subjected to periodic vertical loading”, pp. 105–121, Proc. Int. Symp. Wave Propagation and Dynamic Properties of Earth Materials, Albuquerque, New Mexico, August 1967.

    Google Scholar 

  19. Wong, H.L. and Luco J.E., “Dynamic response of rigid foundations of arbitrary shape”, Earth. Engng. Struct. Dyn., 4, 579–587 (1976).

    Article  Google Scholar 

  20. Gaul, L., “Dynamische Wechselwirkung eines Fundamentes mit dem viscoelastischen Halbraum”, Ing. Arch., 46, 401–422 (1977).

    MATH  Google Scholar 

  21. Kitamura, Y. and Sakurai, S., “Dynamic stiffness for rectangular rigid foundations on a semi-infinite elastic medium”, Int., J. Num. Anal. Meth. Geomech., 3, 159–171 (1979).

    Article  Google Scholar 

  22. Kitamura, Y. and Sakurai, S., “A numerical method for determining dynamic stiffness”, pp. 393–399, Eisenstein, Z, Ed., “Numerical Methods in Geomechanics, Edmonton 1982”, Balkema, Rotterdam, 1982.

    Google Scholar 

  23. Adeli, H., Hejazi, M.S., Keer, L.M. and Nemat-Nasser, S., “Dynamic response of foundations with arbitrary geometries”, Proc. ASCE, 107, EM5, 953–967 (1981).

    Google Scholar 

  24. Hamidzadeh-Eraghi, H.R. and Grootenhuis, P., “The dynamics of a rigid foundation on the surface of an elastic half-space”, Earth. Engng. Struct. Dyn, 9, 501–515 (1981).

    Article  Google Scholar 

  25. Savidis, S.A. and Richter, T, “Dynamic interaction of rigid foundations”, pp. 369–374, Proc. 9th Int. Conf. Soil Mech. Found. Engng, Vol. 2, Tokyo, Japan, 1977.

    Google Scholar 

  26. Gantayat, A. and Kamil, H, “An impedance function approach for soil-structure interaction analyses including structure-to-structure interaction effects”, Trans. 6th SMiRT, Paris, August 1981.

    Google Scholar 

  27. Wong, H.L. and Luco, J.E, “Dynamic response of rectangular foundations in obliquely incident seismic waves”, Earth. Engng. Struct. Dyn, 6, 3–16 (1978).

    Article  Google Scholar 

  28. Luco, J.E. and Wong, H.L, “Dynamic response of rectangular foundations for Rayleigh wave excitation”, pp. 1542–1548, Proc. 6th World Conf. Earth. Engng, N. Delhi, India, 1977.

    Google Scholar 

  29. Bielak, J. and Coronato, J.A, “Response of multiple-mass systems to nonvertically incident seismic waves”, pp. 801–804, Proc. Int. Cont. Recent Advances in Geotech. Earth. Engng. and Soil Dyn, St. Louis, Univ. of Missouri-Rolla, 1981.

    Google Scholar 

  30. Werner, S.D, Lee, L.C, Wong, H.L. and Trifunac, M.D, “Structural response to travelling seismic waves”, Proc. ASCE, 105, ST 12, 2547–2564 (1979).

    Google Scholar 

  31. Luco, J.E. and Wong, H.L, “Response of structures to nonvertically incident seismic waves”, Bull. Seism. Soc. Amer, 72, 275–302 (1982).

    Google Scholar 

  32. Roesset, J.M. and Gonzalez, J.J, “Dynamic interaction between adjacent structures”, pp. 127–166, Vol. 1, Prange, B, Ed, “Dynamical Methods in Soil and Rock Mechanics”, Balkema, Rotterdam, 1978.

    Google Scholar 

  33. Gupta, S, Penzien, J, Lin, T.W. and Yeh, C.S, “Three-dimensional hybrid modeling of soil-structure interaction”, Earth. Engng. Struct. Dyn. 10, 69–87 (1982).

    Article  Google Scholar 

  34. Dasgupta, S.P. and Rao, N.S.V.K, “Dynamics of rectangular footings by finite elements”, Proc. ASCE, 104, GT5, 621–637 (1978).

    Google Scholar 

  35. Roesset, J.M. and Ettouney, M.M., “Transmitting boundaries: a comparison”, Int. J. Num. Anal. Meth. Geomech., 1, 151–176 (1977).

    Article  Google Scholar 

  36. Kausel, E. and Tassoulas, J.L., “Transmitting boundaries: a closed form comparison”, Bull. Seism. Soc. Amer., 71,143–159 (1981).

    MathSciNet  Google Scholar 

  37. Bettess, P. and Zienkiewicz, O.C., “Diffraction and refraction of surface waves using finite and infinite elements”, Int. J. Num. Meth. Engng., 11,1271–1290 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  38. Chow, Y.K. and Smith, I.M., “Infinite elements for dynamic foundation analysis”, pp. 15–22, Vol. 1, Eisenstein, Z., Ed., “Numerical Methods in Geo-Mechanics, Edmonton 1982”, Balkema, Rotterdam, 1982.

    Google Scholar 

  39. Gutierrez, J.A. and Chopra, A.K., “A substructure method for earthquake analysis of structures including structure-soil interaction”, Earth. Engng. Struct. Dyn., 6, 51–69 (1978).

    Article  Google Scholar 

  40. Chopra, A.K., Chakrabarti, P. and Dasgupta, G., “Dynamic stiffness matrices for viscoeleastic half- plane foundations” Proc. ASCE, 102, EM3, 497–514 (1976) and Proc. ASCE, 705, EM5, 729–745 (1979).

    Google Scholar 

  41. Nelson, I. and Isenberg, J., “Soil island approach to structure-media interaction”, pp. 41–57, in Desai, C.S., Ed., “Numerical Methods in Geomechanics”, ASCE, N.Y., 1976.

    Google Scholar 

  42. Day, S.M. and Frazier, G.A., “Seismic response of hemisperical foundation”, Proc. ASCE,105, EMI, 29–41 (1979).

    Google Scholar 

  43. Dasgupta, G., “Foundation impedance matrices for embedded structures by substructure deletion”, Proc. ASCE, 106 EM3, 517–523 (1980).

    Google Scholar 

  44. Dasgupta, G., “A finite element formulation for unbounded homogeneous continua”, J. Appl. Mech., 49, 136–140(1982).

    Google Scholar 

  45. Murakami, H., Shioya, S., Yamada, R. and Luco, J.E., “Transmitting boundaries for time-harmonic elastodynamics on infinite domains”, Int. J. Num. Meth. Engng., 17, 1697–1716 (1981).

    Article  MATH  Google Scholar 

  46. Hadjian, A.H., Luco, J.E. and Tsai, N.C., “Soil-structure interaction: continuum or finite element?”, Nucl. Engng. Des., 31, 151–167 (1974).

    Article  Google Scholar 

  47. Seed, H.B., Lysmer, J. and Hwang, R., “Soil-structure interaction analyses for seismic response”, Proc. ASCE, 101, GT5, 439–457 (1975).

    Google Scholar 

  48. Ang, A.H.S. and Newmark, N.M., “Computation of underground structural response”, Univ. of Illinois Report for Defense Atomic Support Agency (now Defense Nuclear Agency), DASA Rept. 1386, Washington, D.C., June 1963.

    Google Scholar 

  49. Wilkins, M.L., et al., “A method for computer simulation of problems in solid mechanics and gas dynamics in three dimensions and time”, Report UCRL-51574, Lawrence Livermore Laboratory, Univ. of California, 1974.

    Book  Google Scholar 

  50. Robinson, A.R., “The transmitting boundary-again”, pp. 163–177, in Hall, W.J., Ed., “Structural and Geotechnical Mechanics”, Prentice Hall, Englewood Cliffs, N.J., 1977.

    Google Scholar 

  51. Cundal, P.A., Kunar, R.R., Carpenter, P.C. and Marti, J., “Solution of infinite dynamic problems by finite modeling in the time domain”, Proc. 2nd Int. Conf. on Applied Numerical Modelling, Madrid, Spain, Sept. 11–18, 1978.

    Google Scholar 

  52. Kunar, R.R. and Rodriguez-Ovefero, L., “A model with non-reflecting boundaries for use in explicit soil-structure interaction analyses”, Earth. Engng. Struct. Dyn., 8, 361–374 (1980).

    Article  Google Scholar 

  53. Dominguez, J., “Dynamic stiffness of rectangular foundations”, Publ. No. R78–20, Dept. of Civil Engng., M.I.T., August 1978.

    Google Scholar 

  54. Dominguez, J., “Response of embedded foundations to travelling waves”, Publ. No. R78–24, Dept. of Civil Engng., M.I.T., August 1978.

    Google Scholar 

  55. Ottenstreuer, M. and Schmid, G., “Boundary elements applied to soil-foundation interaction”, pp. 293–309 in Proc. 3rd Int. Sem. on Recent Advances in Boundary Element Methods, Irvine, Calif., July 1981.

    Google Scholar 

  56. Ottenstreuer, M., “Frequency dependent dynamic response of footings”, pp. 799–809 in Proc. Soil Dynamics and Earth. Engng. Conf., Southampton, England, July 1982.

    Google Scholar 

  57. Apsel, R.J., “Dynamic Green’s functions for layered media and applications to boundary value problems”, Ph.D. Thesis, Univ. of California, San Diego, Calif., 1979.

    Google Scholar 

  58. Wolf, J.P. and Darbre, G.R., “Dynamic-stiffness matrix of soil by the boundary-element method: conceptual aspects”, Earth. Engng. Struct. Dyn., 12, 385–400 (1984).

    Article  Google Scholar 

  59. Wolf, J.P. and Darbre, G.R., “Dynamic-stiffness matrix of soil by the boundary-element method: embedded foundation”, Earth. Engng. Struct. Dyn., 12, 401–416 (1984).

    Article  Google Scholar 

  60. Karabalis, D.L. and Beskos, D.E, “Dynamic response of 3-D rigid surface foundations by time domain boundary element method”, Earth. Engng. Struct. Dyn, 12, 73–93 (1984).

    Article  Google Scholar 

  61. Karabalis, D.L. and Beskos, D.E., “Earthquake response of 3-D foundations by the boundary element method”, pp. 769–776, Proc. 8th World Conf. Earth. Engng, San Francisco, U.S.A., 1984.

    Google Scholar 

  62. Karabalis, D.L. and Beskos, D.E., “Dynamic response of 3-D flexible foundations by time domain BEM and FEM”, Int. J. Soil Dyn. Earth. Engng, Vol. 4, pp. 91–101,1985.

    Article  Google Scholar 

  63. Zienkiewicz, O.C, Kelly, D.W. and Bettess, P, “The coupling of finite element and boundary solution procedures”, Int. J. Num. Meth. Engng, 11, 355–376 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  64. Kelly, D.W., Mustoe, G.G.W. and Zienkiewicz, O.C, “Coupling boundary element methods with other numerical methods”, pp. 251–285, Banerjee, P.K. and Butterfield, R, Eds, Development in Boundary Element Methods-1, Applied Science Publishers, Ltd, 1979.

    Google Scholar 

  65. Varadarajan, A. and Singh, R.B, “Analysis of tunnels by coupling FEM with BEM”, pp. 611–618, Eisenstein, Z, Ed, Numerical Methods in Geomechanics Edmonton 1982, Balkema, Rotterdam, 1982.

    Google Scholar 

  66. Mita, A. and Takanashi, W, “Dynamic soil-structure interaction analysis by hybrid method”, pp. 785–794, Brebbia, C.A, Futagami, T. and Tanaka, M, Eds, Proc. 5th Int. Conf. in Boundary Elements, Hiroshima, Japan, 1983.

    Google Scholar 

  67. Veletsos, A.S. and Verbic, B, “Basic response functions for elastic foundations”, J. Eng. Mech. Div, ASCE, 100, 189–202 (1974).

    Google Scholar 

  68. Eringen, A.C. and Suhubi, E.S, “Elastodynamics-Vol. II, Linear Theory”, Academic Press, New York, 1975.

    MATH  Google Scholar 

  69. Cruse, T.A. and Rizzo, F.J, “A direct formulation and numerical solution of the general transient elastodynamic problem I”, J. Math. Anal. Appl, 22, 244–259 (1968).

    Article  MATH  Google Scholar 

  70. Cruse, T.A, “A direct formulation and numerical solution of the general transient elastodynamic problem II”, J. Math. Anal. Appl, 22, 341–355 (1968).

    Article  MATH  Google Scholar 

  71. Manolis, G.D. and Beskos, D.E., “Dynamic stress concentration studies by boundary integrals and Laplace transform”, Int. J. Numer. Methods Eng., 17, 573–599 (1981).

    Article  MATH  Google Scholar 

  72. Johnson, L.R, “Green’s function for Lamb’s problem,” Geophys. J.R. Astr. Soc, 37, 99–131 (1974).

    Article  MATH  Google Scholar 

  73. Kobayashi, S. and Nishimura, N, “Green’s tensors for elastic half-spaces. - An application of Boundary Integral Equation Method”, Memoirs of the Faculty of Engineering, Kyoto University, 42, part 2, 228–241 (1980).

    Google Scholar 

  74. Thau, S.A., “Radiation and scattering from a rigid inclusion in an elastic medium”, J. Appl. Mech, ASME, 34, 509–511 (1967).

    Article  Google Scholar 

  75. Kausel, E, Whitman, R.V, Morray, J.P. and Elsabee, F, “The spring method for embedded foundations”, Nucl. Engng. Des, 48, pp. 377–392 (1978).

    Article  Google Scholar 

  76. Whitman, R.V. and Bielak, J, “Foundations”, pp. 223–260, Rosenblueth, E, Ed, Design of Earthquake Resistant Structures, John Wiley & Sons, New York, 1980.

    Google Scholar 

  77. Karabalis, D.L. and Beskos, D.E., “Dynamic Analysis of 3-D rigid embedded foundations by time domain boundary element method,” Computer Methods in Applied Mechanics and Engineering Vol. 56, pp. 91–119, 1986.

    Article  MATH  Google Scholar 

  78. Gaitanaros, A.P. and Karabalis, D.L, “3-D flexible embedded machine foundations by the BEM and the FEM,” pp. 81–96, in: Karabalis, D.L, Ed, “Recent Applications in Computational Mechanics,” ASCE, New York, 1986.

    Google Scholar 

  79. Karabalis, D.L. and Mohammadi, M, “The application of the Boundary Element Method to dynamic soil-structure interaction problems: Computational aspects,” pp. 321–328, Proceedings of the XIII Southeastern Conference on Theoretical and Applied Mechanics, Columbia, South Carolina, April 1986.

    Google Scholar 

  80. Karabalis, D.L. and Beskos, D.E., “Dynamic soil-structure interaction,” Chapter 11, in Beskos D.E., Ed, “Boundary Element Methods in Mechanics,” North-Holland, Amsterdam, 1987.

    Google Scholar 

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Karabalis, D.L., Beskos, D.E. (1987). Three-Dimensional Soil-Structure Interaction by Boundary Element Methods. In: Brebbia, C.A. (eds) Applications in Geomechanics. Topics in Boundary Element Research, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83012-9_1

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  • DOI: https://doi.org/10.1007/978-3-642-83012-9_1

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