Skip to main content
Log in

Vibration isolation using open or filled trenches

Part 3: 2-D non-homogeneous soil

  • Published:
Computational Mechanics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Apsel, R. J. (1979): Dynamic Green's functions for layered media and applications to boundary-value problems, Ph.D. thesis, University of California, San Diego

  • Apsel, R. J.; Luco, J. E. (1983): On the Green's functions for a layered half-space: Part II. Bull. Seismol. Soc. Am. 73, 931–951

    Google Scholar 

  • 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, 213–231

    Google Scholar 

  • 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, 1041–1060

    Google Scholar 

  • Beskos, D. E. (1987): Boundary element methods in dynamic analysis. Appl. Mech. Rev. 40, 1–23

    Google Scholar 

  • 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, 43–63

    Google Scholar 

  • 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: ASCE

    Google Scholar 

  • Chapel, F. (1987): Boundary element method applied to linear soil-structure interaction on a heterogeneous soil. Earthquake Eng. Struct. Dyn. 15, 815–829

    Google Scholar 

  • 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. Balkema

    Google Scholar 

  • 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, 129–142

    Google Scholar 

  • Ewing, W. M.; Jardetzky, W. S.; Press, F. (1957): Elastic waves in layered media. New York: McGraw-Hill

    Google Scholar 

  • Gazetas, G. (1980): Static and dynamic displacements of foundations on heterogeneous multilayered soils. Geotechnique 30, 159–177

    Google Scholar 

  • Gazetas, G.; Roesset, J. M. (1979): Vertical vibrations of machine foundations. J. Geotechn. Eng. Div. ASCE 105, 1435–1454

    Google Scholar 

  • Gupta, R. N. (1966): Reflection of elastic waves from a linear transition layer. Bull. Seismol. Soc. Am. 56, 511–526

    Google Scholar 

  • 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, 627–679

    Google Scholar 

  • Haskell, N. A. (1953): The dispersion of surface waves in multilayered media. Bull. Seismol. Soc. Am. 43, 17–34

    Google Scholar 

  • Herrmann, R. B.; Wang, C. Y. (1985): A comparison of synthetic seismograms. Bull. Seismol. Soc. Am. 75, 41–56

    Google Scholar 

  • Hook, J. F. (1961): Separation of the vector wave equation of elasticity for certain types of inhomogeneous isotropic media. J. Acoust. Soc. Am. 33, 302–313

    Google Scholar 

  • 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, 354–355

    Google Scholar 

  • 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: ASCE

    Google Scholar 

  • Kausel, E.; Peek, R. (1982): Dynamic loads in the interior of a layered stratum: An explicit solution. Bull. Seismol. Soc. Am. 72 1459–1481

    Google Scholar 

  • Kausel, E.; Roesset, J. M. (1981): Stiffness matrices for layered soils. Bull. Seismol. Soc. Am. 71, 1743–1761

    Google Scholar 

  • Kausel, E.; Roesset, J. M.; Waas, G. (1975): Dynamic analysis of footings on layered media. J. Eng. Mech. Div. ASCE 101. 679–693

    Google Scholar 

  • 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, 1415–1437

    Google Scholar 

  • Kobayashi, S. (1987): Elastodynamics. In: Beskos, D. E. (ed): Boundary element methods in mechanics pp. 192–255. Amsterdam: North-Holland

    Google Scholar 

  • Kundu, T.; Mal, A. K. (1985): Elastic waves in a multi-layered solid due to a dislocation source. Wave Motion. 7, 459–471

    Google Scholar 

  • Leung, K. L. (1989): Vibration isolation of structures from ground-transmitted waves in non-homogeneous elastic soil. Ph.D. thesis, University of Minnesota, Minneapolis

  • 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: Elsevier

    Google Scholar 

  • 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)

  • Luco, J. E. (1974): Impedance functions for a rigid foundation on a layered medium. Nucl. Eng. Des. 31, 204–217

    Google Scholar 

  • Luco, J. E. (1976): Vibrations of a rigid disc on a layered viscoelastic medium. Nucl. Eng. Des. 36, 325–340

    Google Scholar 

  • Luco, J. E.; Apsel, R. J. (1983): On the Green's functions for a layered half-space: Part I. Bull. Seismol. Soc. Am. 73, 909–929

    Google Scholar 

  • Luco, J. E.; Wong, H. L. (1987): Seismic response of foundations embedded in a layered half-space. Earthquake Eng. Struct. Dyn. 15, 233–247

    Google Scholar 

  • Manolis, G. D.; Beskos, D. E. (1988): Boundary element methods in elastodynamics. London: Unwin-Hyman

    Google Scholar 

  • May, T. W.; Bolt, B. A. (1982): The effectiveness of trenches in reducing seismic motion. Earthqake Eng. Struct. Dyn. 10, 195–210

    Google Scholar 

  • Meissner, E. (1921): Elastische oberflachenwellen mit dispersion in einen inhomogenen medium. Vierteljahrschr. Naturforsch. Ges. 66, 181–195.

    Google Scholar 

  • Rao, C. R. A. (1967): Separation of the stress equations of motion in nonhomogeneous isotropic elastic media. J. Acoust. Soc. Am. 41, 612–614

    Google Scholar 

  • Rao, C. R. A. (1970): On the integration of the axi-symmetric stress equations of motion for nonhomogeneous elastic media. Arch. Mech. 22, 63–73

    Google Scholar 

  • 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: Wiley

    Google Scholar 

  • RichartJr., F. E.; HallJr., J. R.; Woods, R. D. (1970): Vibrations of soils and foundations. Englewood Cliffs, NJ: Prentice Hall

    Google Scholar 

  • Segol, G.; Lee, P. C. Y.; Abel, J. F. (1978). Amplitude reduction of surface waves by trenches. J. Eng. Mech. Div. ASCE 104, 621–641

    Google Scholar 

  • Stoneley, R. (1936): The transmission of Rayleigh waves in a heterogeneous medium. Geophys. Suppl. Roy. Astron. Soc. 3, 222–232

    Google Scholar 

  • 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, Cambridge

    Google Scholar 

  • Thomson, W. T. (1950): Transmission of elastic waves through a stratified soil medium. J. Appl. Phys. 21, 89–93

    Google Scholar 

  • Vardoulakis, I. (1981): Surface waves in a half-space of submerged sand. Earthquake Eng. Struct. Dyn. 9, 329–342

    Google Scholar 

  • Waas, G. (1972): Linear two-dimensional analysis of soil dynamics problems in semi-infinite layered media. Ph.D. thesis, University of California, Berkeley

  • Wolf, J. P. (1985). Dynamic soil-structure interaction. Englewood Cliffs, NJ: Prentice Hall

    Google Scholar 

  • 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, 1823–1837

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by S. N. Atluri, December 8, 1989

Rights and permissions

Reprints and permissions

About this article

Cite this article

Leung, K.L., Beskos, D.E. & Vardoulakis, I.G. Vibration isolation using open or filled trenches. Computational Mechanics 7, 137–148 (1990). https://doi.org/10.1007/BF00375927

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00375927

Keywords

Navigation