Skip to main content

Wave Scattering in a Laterally Inhomogeneous, Cracked Poroelastic Finite Region

  • Chapter
  • First Online:

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 240))

Abstract

In this chapter, elastic wave propagation in a complex discrete inhomogeneous and heterogeneous geological media is investigated. The new element here is that the medium under consideration is a two-phase material, namely a poroelastic continuum . To simplify the representation, we replace the two-phase material by a single-phase one that exhibits viscoelastic behavior, which is a plausible representation for low-frequency vibrations.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Abascal, R., & Dominguez, J. (1986). Vibrations of footings on zoned viscoelastic soils ASCE. Journal of Engineering Mechanics, 112, 433–447.

    Article  Google Scholar 

  • Apsel, R., & Luco, E. J. (1983). The Green’s functions for a layered half-space Part II. Bulletin of the Seismological Society of America, 73(4), 931–951.

    Google Scholar 

  • Bardet, J. P. (1992). A viscoelastic model for the dynamic behavior of saturated poroelastic soils. ASME. Journal of Applied Mechanics, 59, 128–135.

    Article  MATH  Google Scholar 

  • Bardet, J. P. (1995). The damping of saturated poroelastic soils during steady-state vibrations. Applied Mathematics and Computation, 67, 3–31.

    Article  MATH  Google Scholar 

  • Beskos, D. E., Dasgupta, B., & Vardoulakis, I. G. (1986). Vibration isolation using open or filled trenches. Part I: 2 D homogeneous soil. Computational Mechanics, 1, 43–63.

    Article  MATH  Google Scholar 

  • Biot, M. (1956). Theory of propagation of elastic waves in a fluid-saturated porous solid. The Journal of the Acoustical Society of America, 28(4), 168–191.

    Article  MathSciNet  Google Scholar 

  • CEN. 2004. Eurocode 8: Design Provisions of Structures for Earthquake Resistance. Part 1: General Rules, Seismic Actions and Rules for Buildings. Tech. rept. European Committee for Standardization, Brussels.

    Google Scholar 

  • Cheng, A. H.-D. (2016). Poroelasticity (Vol. 27)., Cham, Switzerland: Theory and Applications of Transport in Porous Media Berlin: Springer International Publishing.

    Google Scholar 

  • Christensen, R. (1971). Theory of Viscoelasticity: An Introduction. New York: Academic Press.

    Google Scholar 

  • Dineva, P. S., & Manolis, G. D. (2001a). Scattering of seismic waves by cracks in multi-layered geological regions: I. Mechanical model. Soil Dynamics and Earthquake Engineering, 21, 615–625.

    Article  Google Scholar 

  • Dineva, P. S., & Manolis, G. D. (2001b). Scattering of seismic waves by cracks in multi-layered geological regions: II. Numerical results. Soil Dynamics and Earthquake Engineering, 21, 627–641.

    Article  Google Scholar 

  • Dineva, P. S., Vaccari, F., & Panza, G. (2003). Hybrid modal summation- BIE method for site effect estimation of a seismic region in a laterally varying media. Journal of Theoretical and Applied Mechanics, 33(4), 55–88.

    MathSciNet  Google Scholar 

  • Dineva, P., Wuttke, F., & Manolis, G. (2012a). Elastic wavefield evaluation in discontinuous poroelastic media by BEM: SH wave. Journal of Theoretical and Applied Mechanics, 42(3), 75–100.

    Article  MathSciNet  Google Scholar 

  • Dineva, P., Datcheva, M., Manolis, G., & Schanz, T. (2012b). Seismic wave propagation in laterally inhomogeneous porous media by BIEM. International Journal of Numerical Analysis of Mathematical Geomechanics, 36(2), 111–127.

    Article  Google Scholar 

  • Kobayashi, S. 1987. Elastodynamics. Pages 191–255 of: Beskos, D. E. (ed), BEM in Mechanics.

    Google Scholar 

  • Lin, C. H., Lee, V. W., & Trifunc, M. D. (2005). The reflection of plane waves in a poroelastic half-space saturated with inviscid fluid. Soil Dynamics and Earthquake Engineering, 25, 205–223.

    Article  Google Scholar 

  • Luco, J. E., & Apsel, R. J. (1983). On the Green‘s functions for layered half-space Part I. Bulletin of the Seismological Society of America, 73, 909–929.

    Google Scholar 

  • Manolis, G. D., & Beskos, D. E. (1981). Dynamic stress concentration studies by boundary integrals and Laplace transform. International Journal for Numerical Methods in Engineering, 17(2), 573–599.

    Article  MATH  Google Scholar 

  • Manolis, G. D., & Beskos, D. E. (1989). Integral formulation and fundamental solutions of dynamic poroelasticity and thermoelasticity. Acta Mechanics, 76, 89–104.

    Article  MATH  Google Scholar 

  • Morochnik, V., & Bardet, J. P. (1996). Viscoelastic approximation of poroelastic media for wave scattering problems. Soil Dynamics and Earthquake Engineering, 15(5), 337–346.

    Article  Google Scholar 

  • Rangelov, T., Dineva, P., & Gross, D. (2003). A hypersingular traction boundary integral equation method for stress intensity factor computation in a finite cracked body. Engineering Analysis with Boundary Elements, 27, 9–21.

    Article  MATH  Google Scholar 

  • Sharma, M. D. (2002). Group velocity along general direction in a general anisotropic medium. International Journal of Solids and Structures, 39, 3277–3288.

    Article  MATH  Google Scholar 

  • Sladek, V., & Sladek, J. (1984). Transient elastodynamic three-dimensional problems in cracked bodies. Aplied Mathematical Modelling, 8, 2–10.

    Article  MathSciNet  MATH  Google Scholar 

  • Wuttke, F. (2005) Advanced site investigation by use of surface waves. Ph.D. thesis, Bauhaus University, Weimar.

    Google Scholar 

  • Wuttke, F., Dineva, P., & Schanz, T. (2011). Seismic wave propagation inlaterally inhomogeneous geologicalregion via a new hybrid approach. Journal of Sound and Vibration, 330, 664–684.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to George D. Manolis .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Manolis, G.D., Dineva, P.S., Rangelov, T.V., Wuttke, F. (2017). Wave Scattering in a Laterally Inhomogeneous, Cracked Poroelastic Finite Region. In: Seismic Wave Propagation in Non-Homogeneous Elastic Media by Boundary Elements. Solid Mechanics and Its Applications, vol 240. Springer, Cham. https://doi.org/10.1007/978-3-319-45206-7_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-45206-7_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45205-0

  • Online ISBN: 978-3-319-45206-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics