Computational Mechanics

, Volume 7, Issue 2, pp 137–148 | Cite as

Vibration isolation using open or filled trenches

Part 3: 2-D non-homogeneous soil
  • K. L. Leung
  • D. E. Beskos
  • I. G. Vardoulakis
Article

Abstract

The problem of isolating structures from surface waves by open or filled trenches under conditions of plane strain is numerically studied. The soil is assumed to be an isotropic, linear elastic or viscoelastic nonhomogeneous (layered) half-space medium. Waves generated by the harmonic motion of a rigid surface machine foundatin are considered. The formulation and solution of the problem are accomplished by the frequency domain boundary element method. The Green's function of Kausel-Peek-Hull for a thin layered half-space is employed and this essentially requires only a discretization of the trench perimeter and the soil-foundation interface. The proposed methodology is used for the solution of a number of vibration isolation problems and the effect of soil inhomogeneity on the wave screening effectiveness of trenches is discussed.

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References

  1. Apsel, R. J. (1979): Dynamic Green's functions for layered media and applications to boundary-value problems, Ph.D. thesis, University of California, San DiegoGoogle Scholar
  2. Apsel, R. J.; Luco, J. E. (1983): On the Green's functions for a layered half-space: Part II. Bull. Seismol. Soc. Am. 73, 931–951Google Scholar
  3. Apsel, R. J.; Luco, J. E. (1987): Impedance functions for foundations embedded in a layered medium: An integral equation approach. Earthquake Eng. Struct. Dyn. 15, 213–231Google Scholar
  4. Banerjee, P. K.; Ahmad, S.; Chen, K. (1988): Advanced application of BEM to wave barriers in multi-layered three-dimensional soil media. Earthquake Eng. Struct. Dyn. 16, 1041–1060Google Scholar
  5. Beskos, D. E. (1987): Boundary element methods in dynamic analysis. Appl. Mech. Rev. 40, 1–23Google Scholar
  6. Beskos, D. E.; Dasgupta, B.; Vardoulakis, I. G. (1986). Vibration isolation using open or filled trenches. Part 1: 2-D homogeneous soil. Comput. Mech. 1, 43–63Google Scholar
  7. Beskos, D. E.; Leung, K. L.; Vardoulakis, I. G. (1986): Vibration isolation of structures from surface waves in layered soil. In: Karabalis, D. L. (ed). Recent applications in computational mechanics, pp. 125–140. New York: ASCEGoogle Scholar
  8. Chapel, F. (1987): Boundary element method applied to linear soil-structure interaction on a heterogeneous soil. Earthquake Eng. Struct. Dyn. 15, 815–829Google Scholar
  9. Chapel, F.; Tsakalidis, C. (1985): Computation of the Green's functions of elastodynamics for a layered half space through a Hankel transformation. Applications to foundation vibration and seismology. In: Kawamoto, T.; Ichikawa, Y. (eds): Numerical methods in geomechanics Nagoya 1985, pp. 1311–1318. Rotterdam: A. A. BalkemaGoogle Scholar
  10. Dasgupta, B.; Beskos, D. E.; Vardoulakis, I. G. (1990): Vibration isolation using open or filled trenches. Part 2: 3-D homogeneous soil. Comput. Mech. 6, 129–142Google Scholar
  11. Ewing, W. M.; Jardetzky, W. S.; Press, F. (1957): Elastic waves in layered media. New York: McGraw-HillGoogle Scholar
  12. Gazetas, G. (1980): Static and dynamic displacements of foundations on heterogeneous multilayered soils. Geotechnique 30, 159–177Google Scholar
  13. Gazetas, G.; Roesset, J. M. (1979): Vertical vibrations of machine foundations. J. Geotechn. Eng. Div. ASCE 105, 1435–1454Google Scholar
  14. Gupta, R. N. (1966): Reflection of elastic waves from a linear transition layer. Bull. Seismol. Soc. Am. 56, 511–526Google Scholar
  15. Harkrider, D. G. (1964): Surface waves in multilayered elastic media-I: Rayleigh and Love waves from burried sources in a multilayered elastic halfspace. Bull. Seismol Soc. Am. 54, 627–679Google Scholar
  16. Haskell, N. A. (1953): The dispersion of surface waves in multilayered media. Bull. Seismol. Soc. Am. 43, 17–34Google Scholar
  17. Herrmann, R. B.; Wang, C. Y. (1985): A comparison of synthetic seismograms. Bull. Seismol. Soc. Am. 75, 41–56Google Scholar
  18. Hook, J. F. (1961): Separation of the vector wave equation of elasticity for certain types of inhomogeneous isotropic media. J. Acoust. Soc. Am. 33, 302–313Google Scholar
  19. Hook, J. F. (1962): Generalization of a method of potentials for the vector wave equation of elasticity for inhomogeneous media. J. Acoust. Soc. Am 34, 354–355Google Scholar
  20. Hull, S. W.; Kausel, E. (1984): Dynamic loads in layered halfspaces. In: Boresi, A. P.; Chong, K. P. (eds): Engineering mechanics in civil engineering, pp. 201–204. New York: ASCEGoogle Scholar
  21. Kausel, E.; Peek, R. (1982): Dynamic loads in the interior of a layered stratum: An explicit solution. Bull. Seismol. Soc. Am. 72 1459–1481Google Scholar
  22. Kausel, E.; Roesset, J. M. (1981): Stiffness matrices for layered soils. Bull. Seismol. Soc. Am. 71, 1743–1761Google Scholar
  23. Kausel, E.; Roesset, J. M.; Waas, G. (1975): Dynamic analysis of footings on layered media. J. Eng. Mech. Div. ASCE 101. 679–693Google Scholar
  24. Kawase, H. (1988): Time-domain response of a semi-circular canyon for incident SV, P and Rayleigh waves calculated by the discrete wavenumber boundary element method. Bull. Seismol. Soc. Am. 78, 1415–1437Google Scholar
  25. Kobayashi, S. (1987): Elastodynamics. In: Beskos, D. E. (ed): Boundary element methods in mechanics pp. 192–255. Amsterdam: North-HollandGoogle Scholar
  26. Kundu, T.; Mal, A. K. (1985): Elastic waves in a multi-layered solid due to a dislocation source. Wave Motion. 7, 459–471Google Scholar
  27. Leung, K. L. (1989): Vibration isolation of structures from ground-transmitted waves in non-homogeneous elastic soil. Ph.D. thesis, University of Minnesota, MinneapolisGoogle Scholar
  28. Leung, K. L.; Vardoulakis, I. G.; Beskos, D. E.;(1987): Vibration isolation of structures from surface waves in homogeneous and nonhomogeneous soils In: Cakmak, A. S. (ed): Soil-structure interaction, pp. 155–169, Amsterdam: ElsevierGoogle Scholar
  29. Leung, K. L.; Vardoulakis, I. G.; Beskos, D. E.; Tassoulas, J. L. (1990): Vibration isolation by trenches in continuously nonhomogeneous soil by the BEM. Soil Dyn. Earthquake Eng. (in press)Google Scholar
  30. Luco, J. E. (1974): Impedance functions for a rigid foundation on a layered medium. Nucl. Eng. Des. 31, 204–217Google Scholar
  31. Luco, J. E. (1976): Vibrations of a rigid disc on a layered viscoelastic medium. Nucl. Eng. Des. 36, 325–340Google Scholar
  32. Luco, J. E.; Apsel, R. J. (1983): On the Green's functions for a layered half-space: Part I. Bull. Seismol. Soc. Am. 73, 909–929Google Scholar
  33. Luco, J. E.; Wong, H. L. (1987): Seismic response of foundations embedded in a layered half-space. Earthquake Eng. Struct. Dyn. 15, 233–247Google Scholar
  34. Manolis, G. D.; Beskos, D. E. (1988): Boundary element methods in elastodynamics. London: Unwin-HymanGoogle Scholar
  35. May, T. W.; Bolt, B. A. (1982): The effectiveness of trenches in reducing seismic motion. Earthqake Eng. Struct. Dyn. 10, 195–210Google Scholar
  36. Meissner, E. (1921): Elastische oberflachenwellen mit dispersion in einen inhomogenen medium. Vierteljahrschr. Naturforsch. Ges. 66, 181–195.Google Scholar
  37. Rao, C. R. A. (1967): Separation of the stress equations of motion in nonhomogeneous isotropic elastic media. J. Acoust. Soc. Am. 41, 612–614Google Scholar
  38. Rao, C. R. A. (1970): On the integration of the axi-symmetric stress equations of motion for nonhomogeneous elastic media. Arch. Mech. 22, 63–73Google Scholar
  39. Rao, C. R. A. (1978): Wave propagation in elastic media with prescribed variation in the parameters. In: Miklowitz, J.; Achenbach, J. D. (eds): Modern problems in elastic wave propagation, pp. 327–343. New York: WileyGoogle Scholar
  40. RichartJr., F. E.; HallJr., J. R.; Woods, R. D. (1970): Vibrations of soils and foundations. Englewood Cliffs, NJ: Prentice HallGoogle Scholar
  41. Segol, G.; Lee, P. C. Y.; Abel, J. F. (1978). Amplitude reduction of surface waves by trenches. J. Eng. Mech. Div. ASCE 104, 621–641Google Scholar
  42. Stoneley, R. (1936): The transmission of Rayleigh waves in a heterogeneous medium. Geophys. Suppl. Roy. Astron. Soc. 3, 222–232Google Scholar
  43. Tassoulas, J. L. (1981): Elements for the numerical analysis of wave motion in layered media. Report R81-2. Dept. of Civil Eng. Massachusetts Institute of Technology, CambridgeGoogle Scholar
  44. Thomson, W. T. (1950): Transmission of elastic waves through a stratified soil medium. J. Appl. Phys. 21, 89–93Google Scholar
  45. Vardoulakis, I. (1981): Surface waves in a half-space of submerged sand. Earthquake Eng. Struct. Dyn. 9, 329–342Google Scholar
  46. Waas, G. (1972): Linear two-dimensional analysis of soil dynamics problems in semi-infinite layered media. Ph.D. thesis, University of California, BerkeleyGoogle Scholar
  47. Wolf, J. P. (1985). Dynamic soil-structure interaction. Englewood Cliffs, NJ: Prentice HallGoogle Scholar
  48. Xu, P. C.; Mal, A. K. (1987): Calculation of the in-plane Green's functions for a layered viscoelastic solid. Bull. Seismol. Soc. Am. 77, 1823–1837Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • K. L. Leung
    • 1
  • D. E. Beskos
    • 2
  • I. G. Vardoulakis
    • 3
  1. 1.Department of Civil and Mineral EngineeringUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of Civil EngineeringUniversity of PatrasPatrasGreece
  3. 3.Department of Civil and Mineral EngineeringUniversity of MinnesotaMinneapolisUSA

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