Skip to main content

The Effect of Voids and Inclusions on Wave Propagation in Granular Materials

  • Chapter
Micromechanics and Inhomogeneity

Abstract

Theoretical and experimental studies have been conducted on the dynamic response of granular materials containing local discontinuities of voids and inhomogeneous inclusions. The granular medium was simulated by a specific assembly of circular disks which were subjected to explosive loadings of short duration. Voids were created by removing particular disks from the assembly, while inclusions were constructed by replacing certain disks with those of a higher impedance material. The computational simulation was accomplished through the use of the distinct element method in which the intergranular contact forces and displacements of the assembly disks are determined through a series of calculations tracing the movements of each of the individual disks. The experimental study employed the use of photoelasticity in conjunction with high-speed photography to collect photographic data of the propagation of waves in transparent assemblies of model granular media. Comparisons were made between the computational results and the experimental data for the local intergranular contact forces around each void or inclusion. Both voids and inclusions produce local wave scattering through various reflection mechanisms, and the results seem to indicate that the inclusions produced higher local wave attenuation.

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

Access this chapter

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 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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bathurst, R. J. and Rothenburg, L. (1988), Micromechanical aspects of isotropic granular assemblies with linear contact interactions, J. Appl. Mech., 55, 17–23.

    Article  ADS  Google Scholar 

  • Bazant, Z. P., Krizek, R. J., and Shieh, C. L. (1983), Hysteretic endochronic theory for sand, J. Engng. Mech., 109, 1073–1095.

    Google Scholar 

  • Brandt, H. (1955), A study of the speed of sound of porous granular media, J. Appl. Mech., 22, 479–486.

    MATH  Google Scholar 

  • Carroll, M. M. and Holt, A. C. (1972), Static and dynamic pore-collapse relations for ductile porous materials, J. Appl. Phys., 43, 1626–1636.

    Article  ADS  Google Scholar 

  • Cundall, P. and Strack, D. L. (1979), A discrete numerical model for granular assemblies, Geotechnique, 29, 47–65.

    Article  Google Scholar 

  • Deresiewicz, H. (1958), Mechanics of granular matter, in Advances in Applied Mechanics, Vol. V, Academic Press, New York.

    Google Scholar 

  • Duffy, J. and Mindlin, R. D. (1957), Stress-strain relations and vibration of granular medium“, J. Appl. Mech.,24 585–593.

    MathSciNet  Google Scholar 

  • Endley, S. N. and Peyrot, A. H. (1977), Load distribution in granular media, J. Engng. Mech. Division of ASCE, 103, 99–111.

    Google Scholar 

  • Fu, L. S. (1984), A new micro-mechanical theory for randomly inhomogeneous media, in Wave Propagation in Homogeneous Media and Ultrasonic Non-Destructive Evaluation, Vol. 62, Applied Mechanics Division, American Society of Mechanical Engineers, New York.

    Google Scholar 

  • Gassman, F. (1951), Elastic waves through a packing of spheres, Geophysics, 16, 673–685.

    Article  ADS  Google Scholar 

  • Goodman, M. A. and Cowin, S. C. (1972), A continuum theory for granular materials, Arch. Rat. Mech. Anal., 44, 249–266.

    Article  MathSciNet  MATH  Google Scholar 

  • Hendron, A. J. (1963), The behavior of sand in one-dimensional compression, Ph.D. Thesis, University of Illinois.

    Google Scholar 

  • Hughes, D. S. and Cross, J. H. (1951), Elastic wave velocities in rocks at high pressures and temperatures, Geophysics, 16, 577–593.

    Article  ADS  Google Scholar 

  • Hughes, D. S. and Kelly, J. L. (1952), Variation of elastic wave velocity with saturation in sandstone, Geophysics, 17, 739–752.

    Article  ADS  Google Scholar 

  • Iida, K. (1939), The velocity of elastic waves in sand, Bull. Earthquake Res. Inst. Japan, 17, 783–808.

    Google Scholar 

  • Nemat-Nasser, S. and Mehrabadi, M. M. (1983), Stress and fabric in granular masses, in Mechanics of Granular Materials: New Models and Constitutive Relations, Elsevier, Amsterdam, pp. 1–8.

    Google Scholar 

  • Nunziato, J. W., Kennedy, J. E., and Walsh, E. (1978), The behavior of one-dimensional acceleration waves in an inhomogeneous granular solid, Int. J. Engng. Sci., 16, 637–648.

    Article  MATH  Google Scholar 

  • Petrakis, E. and Dobry, R. (1986), A self-consistent estimate of the elastic constants of a random array of equal spheres with application to granular soil under isotropic conditions, Report CE-86–04, Rensselaer Polytechnic Institute, Troy, NY.

    Google Scholar 

  • Riley, W. F. and Daily, J. W. (1969), Recording dynamic fringe patterns with a Cranz—Schardin camera, Exp. Mech., 9, 27–33.

    Article  Google Scholar 

  • Sadd, M. H. Shukla, A., and Mei, H (1989), Computational and experimental modeling of wave propagation in granular materials, Proceedings of the 4th International Conference on Computational Methods and Experimental Measurements, Capri, Italy, May, 1989.

    Google Scholar 

  • Sadd, M. H. and Hossain, M. (1989), Wave propagation in distributed bodies with applications to dynamic soild behavior, J. Wave-Material Interaction, to appear.

    Google Scholar 

  • Shukla, A. and Nigam, H. (1985), A numerical-experimental analysis of the contact stress problem, J. Strain Anal., 20, 241–245.

    Article  Google Scholar 

  • Shukla, A. and Damania, C. (1987), Experimental investigation of wave velocity and dynamic contact stresses in an assembly of discs, Exp. Mech., 27, 268–281.

    Article  Google Scholar 

  • Shukla, A., Zhu, C. Y., and Sadd, M. H. (1988), Angular dependence of dynamic load transfer due to explosive loading in granular aggregate chains, J. Strain Anal., 23, 121–127.

    Article  Google Scholar 

  • Takahashi, T. and Sato, Y. (1949), On the theory of elastic waves in granular substance, Bull. Earthquake Res. Inst. Japan, 27, 11–16.

    MathSciNet  Google Scholar 

  • Thornton, C. and Barnes, D. J. (1986), Computer simulated deformation of compact granular assemblies, Acta Mech., 64, 45–61.

    Article  Google Scholar 

  • Walton, K. (1987), The effective elastic moduli of a random packing of spheres, J. Mech. Phys. Solids, 35, 213–226.

    Article  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Sadd, M.H., Shukla, A., Mei, H., Zhu, C.Y. (1990). The Effect of Voids and Inclusions on Wave Propagation in Granular Materials. In: Weng, G.J., Taya, M., Abé, H. (eds) Micromechanics and Inhomogeneity. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8919-4_23

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-8919-4_23

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8921-7

  • Online ISBN: 978-1-4613-8919-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics