Skip to main content
Log in

Vibration isolation using open or filled trenches

Part 1 : 2-D homogeneous soil

  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

The problem of structural isolation from ground transmitted vibrations by open or infilled trenches under conditions of plane strain is numerically studied. The soil medium is assumed to be linear elastic or viscoelastic, homogeneous and isotropic. Horizontally propagating Rayleigh waves or waves generated by the motion of a rigid foundation or by surface blasting are considered in this work. The formulation and solution of the problem is accomplished by the boundary element method in the frequency domain for harmonic disturbances or in conjunction with Laplace transform for transient disturbances. The proposed method, which requires a discretisation of only the trench perimeter, the soil-foundation interface and some portion of the free soil surface on either side of the trench appears to be better than either finite element or finite difference techniques. Some parametric studies are also conducted to assess the importance of the various geometrical, material and dynamic input parameters and provide useful guidelines to the design engineer.

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

  • Aboudi, J. (1971): The motion excited by an impulsive source in an elastic half-space with a surface obstacle. Bull. Seism. Soc. Amer. 61, 747–763

    Google Scholar 

  • Aboudi, J. (1973): Elastic waves in half-space with thin barrier. Proc. ASCE, 99, J. Engng. Mechs. Dir., EMI, 69–83

    Google Scholar 

  • Abramowitch, M.; Stegun, I.R. (1974): Handbook of mathematical functions. New York: Dover

    Google Scholar 

  • Angel, Y.C.; Achenbach, J.D. (1984): Reflection and transmission of obliquely incident Rayleigh waves by a surface-breaking crack. J. Acoust. Soc. Amer. 75, 313–319

    Article  Google Scholar 

  • Avilés, J.; Sánchez-Sesma, F.J. (1983): Piles as barriers for elastic waves. Proc. ASCE 109, No 9, J. Geotechn. Eng., 1133–1146

    Google Scholar 

  • Banerjee, P.K.; Ahmad, S.; Manolis, G.D. (1986): Advanced elastodynamic analysis, Chapter 5. In: Beskos, D.E. (ed) Boundary element methods in mechanics. Amsterdam: North-Holland

    Google Scholar 

  • Barkan, D.D. (1962): Dynamics of bases and foundations. New York: McGraw-Hill

    Google Scholar 

  • Beskos, D.E.; Dasgupta, B.; Vardoulakis, I.G. (1985): Vibration isolation of machine foundations. In: Gazetas, G.; Selig, E.T. (eds): Vibration problems in geotechnical engineering, pp. 138–151, New York: ASCE

    Google Scholar 

  • Chu, L.L.; Askar, A.; Cakmak, A.S. (1982): An approximate method for scattering in elastodynamics — The born approximation, I: the general formulation; II: SH-waves in infinite and half-space. Soil Dyn. Earth Engng. 1, 59–66, 102-116

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Dasgupta, B. (1986): Vibration isolation of structures on homogeneous soil. Ph. D. Thesis, University of Minnesota, Minneapolis, Minnesota

    Google Scholar 

  • Dolling, H.J. (1965): Schwingungsisolierung von Bauwerken durch tiefe auf geeignete Weise stabilisierte Schlitze. VDI-Ber. 88, 3741

    Google Scholar 

  • Dolling, H.J. (1970a): Die Abschirmung von Erschutterungen durch Bodenschlitze. Bautechnik 47, 151–158

    Google Scholar 

  • Dolling, H.J. (1970b): Die Abschirmung von Erschütterungen durch Bodenschlitze. Bautechnik 47, 194–204

    Google Scholar 

  • Dominguez, J. (1978): Response of embedded foundations to travelling waves. Rep. R78-24, Dept. of Civil Engng., M.I.T.

  • Dominguez, J.; Alarcon, E. (1981): Elastodynamics. In: Brebbia, C.A. (ed): Progress in boundary element methods, Vol. 1, pp. 213–257. London: Pentech Press

    Google Scholar 

  • Dravinski, M.; Than, S.A. (1976a): Multiple diffractions of elastic waves by a rigid rectangular foundation: Plane strain model. J. Appl. Mech. 43, 291–294

    Article  Google Scholar 

  • Dravinski, M.; Thau, S.A. (1976b): Multiple diffractions of elastic shear waves by a rigid rectangular foundation embedded in an elastic half-space. J. Appl. Mech. 43, 295–299

    Article  Google Scholar 

  • Dravinski, M. (1980): Scattering of elastic waves by an alluvial valley of arbitrary shape. Rep. No. CE 80-06, Dept. of Civil Engng., Univ. of Southern California, Los Angeles, California

    Google Scholar 

  • Dravinski, M. (1982a): Scattering of SH waves by subsurface topography. Proc. ASCE 108, J. Engng. Mechs. Dir., EMI, 1–17

    Google Scholar 

  • Dravinski, M. (1982b): Scattering of elastic waves by an alluvial valley. Proc. ASCE 108, J. Engng. Mechs. Dir., EMI, 19–31

    Google Scholar 

  • Dravinski, M. (1982c): Influence of interface depth upon strong ground motion. Bull. Seism. Soc. Amer. 72, 597–614

    Google Scholar 

  • Durbin, F. (1974): Numerical inversion of Laplace transforms: an efficient improvement to Dubner's and Abate's method. Computer J. 17, 371–376

    Article  MathSciNet  Google Scholar 

  • Emad, K.; Manolis, G.D. (1985): Shallow trenches and propagation of surface waves. J. Engng. Mech., ASCE 111, 279–282

    Article  Google Scholar 

  • Fuyuki, M.; Matsumoto, Y. (1980): Finite difference analysis of Rayleigh wave scattering at a trench. Bull. Seism. Soc. Amer. 70, 2051–2069

    Google Scholar 

  • Haupt, W.A. (1977): Isolation of vibrations by concrete core walls. Proc. 9th Int. Conf. Soil Mech. Found. Engng. Tokyo, 2, 251–256

    Google Scholar 

  • Haupt, W.A. (1978a): Numerical methods for the computation of steady-state harmonic wave fields. In: Prange, B. (ed): Dynamical methods in soil and rock mechanics, pp 255–280. Rotterdam: Balkema

    Google Scholar 

  • Haupt, W.A. (1978b): Surface waves in non-homogeneous half-space. In: Prange, B. (ed): Dynamical methods in soil and rock mechanics, pp 335–367. Rotterdam: Balkema

    Google Scholar 

  • Haupt, W.A. (1978c): Behaviour of surface waves in in-homogeneous half-space with special consideration of wave isolation, (in german). Ph. D. thesis, University of Karlsruhe

  • Hudson, J.A. (1967): Scattered surface waves from a surface obstacle. Geophys. J. R. Astr. Soc. 13, 441–458

    Article  Google Scholar 

  • Karabalis, D.L.; Beskos,D.E.: Dynamic response of 3-D rigid embedded foundations by the boundary element method. Comp. Meth. Appl. Mech. Eng. (To appear)

  • Knopoff, L. (1959a): Scattering of compression waves by spherical obstacles. Geophysics 24, 30–39

    Article  MathSciNet  Google Scholar 

  • Knopoff, L. (1959b): Scattering of shear waves by spherical obstacles. Geophysics 24, 209–219

    Article  MathSciNet  Google Scholar 

  • Kobayashi, S.; Nishimura, N. (1982): Transient stress analysis of tunnels and cavities of arbitrary shape due to travelling waves. In: Banerjee, P.K.; Shaw, R.P. (eds.): Developments in boundary element methods-2, pp 177–210. London: Applied Sci.

    Google Scholar 

  • Lee, V.W. (1982): A note on the scattering of elastic plane waves by a hemispherical canyon. Soil Dyn. Earth. Eng. 1, 122–129

    Google Scholar 

  • Liao, S.; Sangrey, D.A. (1978): Use of piles as isolation barriers. Proc. ASCE 104, J. Geotech. Engng. Dir., GT9, 1139–1152

    Google Scholar 

  • Luco, J.E. (1969): Dynamic interaction of a shear wall with the soil. Proc. ASCE 95, J. Engng. Mechs. Dir., EM2, 333–346

    Google Scholar 

  • Luco, J.E. (1976): Torsional response of structures for SH waves: the case of hemispherical foundations. Earth. Eng. Struct. Dyn. 66, 109–123

    Google Scholar 

  • Luco, J.E.; Wong, H.L.; Trifunac, M.D. (1975): A note on the dynamic response of rigid embedded foundations. Earth. Eng. Struc. Dyn. 4, 119–127

    Article  Google Scholar 

  • Mal, A.K.; Knopoff, L. (1975): Transmission of Rayleigh waves past a step change in elevation. Bull. Seism. Soc. Amer. 55, 319–334

    Google Scholar 

  • Manolis, G.D.; Beskos, D.E. (1981): Dynamic stress concentration studies by boundary integrals and Laplace transform. Int. J. Num. Meth. Eng. 17, 573–599

    Article  Google Scholar 

  • Manolis, G.D.; Beskos, D.E. (1983): Dynamic response of lined tunnels by an isoparametric boundary element method. Comp. Meth. Appl. Mech. Eng. 36, 291–307

    Article  Google Scholar 

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

    Article  Google Scholar 

  • McNeill, R. L.; Margason, B.E.; Babcock, F.M. (1965) : The role of soil dynamics in the design of stable test pads, pp 366–375. Guidance and Control Conference, Minneapolis, Minnesota

  • Mei, C.C.; Foda, M.A. (1979): An analytical theory of resonant scattering of SH waves by thin overground structures. Earth. Eng. Struct. Dyn. 7, 335–353

    Article  Google Scholar 

  • Mendelsohn, D.A.; Achenbach, J.D.; Keer, L.M. (1980): Scattering of elastic waves by a surface-breaking crack. Wave Motion 2, 277–292

    Article  Google Scholar 

  • Miller, G.F.; Pursey, H. (1955): On the partition of energy between elastic waves in a semi-infinite solid. Proc. Roy. Soc. London, A 233, 55–69

    MATH  Google Scholar 

  • Narayanan, G.V.; Beskos, D.E. (1982): Numerical operational methods for time dependent linear problems. Int. J. Num. Meth. Eng. 18, 1829–1854

    Article  MathSciNet  Google Scholar 

  • Neumeuer, H. (1963): Untersuchungen über die Abschirmung eines bestehenden Gebäudes gegen Erschütterungen beim Ban und Betrieb einer U-Bahnstrecke. Baumaschine and Bautechnik 10, 23–29

    Google Scholar 

  • Pao, Y.H.; Mow, C.C. (1963): Scattering of plane compressional waves by a spherical obstacle. J. Appl. Phys. 34, 493–499

    Article  MathSciNet  Google Scholar 

  • Pao, Y.H.; Mow, C.C. (1973): Diffraction of elastic waves and dynamic stress concentrations. New York: Crane Russak

    Book  Google Scholar 

  • Richart, Jr., F.E.; Hall, Jr., J.R.; Woods, R.D. (1970): Vibrations of soils and foundations. Englewood Cliffs, N.J.: Prentice Hall

    Google Scholar 

  • Rizzo,F.J.; Shippy,D.J.; Rezayat,M. (1985a): Boundary integral equation analysis for a class of earth-structure interaction problems. Rep. to NSF, Dept. of Engg. Mechs. University of Kentucky

  • Rizzo, F.J.; Shippy, D.J.; Rezayat, M. (1985b): A boundary integral equation method for radiation and scattering of elastic waves in 3-dimensions. Int. J. Num. Meth. Eng. 21, 115–129

    Article  Google Scholar 

  • Sánchez-Sesma, F.J.; Esquivel, J.A. (1979): Ground motion on alluvial valleys under incident plane SH waves. Bull. Seism. Soc. Amer. 69, 1107–1120

    Google Scholar 

  • Sánchez-Sesma, F.J.; Rosenblueth, E. (1979): Ground motion at canyons of arbitrary shape under incident SH wave. Earth. Eng. Struct. Dyn. 7, 441–450

    Article  Google Scholar 

  • Sánchez-Sesma, F.J. (1983): Diffraction of elastic waves by three-dimensional surface irregularities. Bull. Seism. Soc. Amer. 73, 1621–1636

    Google Scholar 

  • Segol, G.; Lee, P.C.Y.; Abel, J.F. (1978): Amplitude reduction of surface waves by trenches. Proc. ASCE 104, J. Engng. Mechs. Dir., EM3, 621–641

    Google Scholar 

  • Spyrakos, C.C. ; Beskos, D.E. : Dynamic response of rigid strip foundations by time domain boundary element method. Int. J. Num. Method. Eng. (To appear)

  • Stroud, A.H.; Secrest, D. (1966): Gaussian quadrature formulas. Englewood Cliffs, N.J.: Prentice Hall

    MATH  Google Scholar 

  • Thau, S.A.; Pao, Y.H. (1966): Diffractions of horizontal shear waves by a parabolic cylinder and dynamic stress concentrations. J. Appl. Mech. 33, 785–792

    Article  Google Scholar 

  • Thau, S.A.; Umek, A. (1973): Transient response of a burried foundation to anti-plane shear waves. J. Appl. Mech. 40, 1061–1066

    Article  Google Scholar 

  • Thau, S.A.; Umek, A. (1974): Coupled rocking and translating vibrations of a burried foundation. J. Appl. Mech. 41, 697–702

    Article  Google Scholar 

  • Trifunac, M.D. (1973): Scattering of plane SH waves by a semicylindrical canyon. Earth. Eng. Struct. Dyn. 1, 267–281

    Article  Google Scholar 

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

    Google Scholar 

  • Woods, R.D. (1967): Screening of elastic surface waves by trenches. Ph.D. thesis, University of Michigan, Ann Arbor, Michigan

    Google Scholar 

  • Woods, R.D. (1968): Screening of surface waves in soils. Proc. ASCE 94, J. Soil Mechs. Found. Engng. Dir., SM4, 951–979

    Google Scholar 

  • Woods, R.D.; Barnett, N.E.; Sagesser, R. (1974): Holography, a new tool for soil dynamics. Proc. ASCE 100, J. Geotech. Engng. Dir., GT11, 1231–1247

    Google Scholar 

  • Woods, R.D.; Richart, Jr., F.E. (1967): Screening of elastic surface waves by trenches. Proc. Int. Symp. on Wave Propagation and Dynamic Properties of Earth Materials, Albuquerque, N.M.

  • Wong, H.L.; Jennings, P.C. (1975): Effects of canyon topography on strong ground motion. Bull. Seism. Soc. Amer. 65, 1239–1257

    Google Scholar 

  • Wong, H.L.; Trifunac, M.D. (1974): Scattering of plane SH waves by a semielliptical canyon. Earth. Eng. Struct. Dyn. 3, 157–169

    Article  Google Scholar 

  • Wong, H.L.; Trifunac, M.D.; Westermo, B. (1977): Effects of surface and subsurface irregularities on the amplitude of monochromatic waves. Bull. Seism. Soc. Amer. 67, 353–368

    Google Scholar 

  • Wong, H.L. (1982): Effect of surface topography on the diffraction of P, SV and Rayleigh waves. Bull. Seism. Soc. Amer. 72, 1167–1183

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by S. N. Atluri, December 26, 1985

Rights and permissions

Reprints and permissions

About this article

Cite this article

Beskos, D.E., Dasgupta, B. & Vardoulakis, I.G. Vibration isolation using open or filled trenches. Computational Mechanics 1, 43–63 (1986). https://doi.org/10.1007/BF00298637

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00298637

Keywords

Navigation