Advertisement

Applied Mathematics and Mechanics

, Volume 36, Issue 6, pp 763–776 | Cite as

Comparison about parametric effects on wave propagation characteristics

  • Zhijun Liu
  • Tangdai XiaEmail author
  • Qingqing Zheng
  • Weiyun Chen
Article
  • 63 Downloads

Abstract

The frequency effects on the velocities and attenuations of the bulk waves in a saturated porous medium are numerically studied in the cases of considering and neglecting the compressibility of solid grain, respectively. The results show that the whole frequency can be divided into three parts, i.e., low frequency band, medium frequency band, and high frequency band, according to the variation curves and the characteristic frequency. The compressibility of the solid grain affects the P 1 wave distinctively, the S wave tiny, and the P 2 wave little. The effects of the porosity and Poisson’s ratio on the bulk waves are numerically analyzed. It is found that both the porosity and Poisson’s ratio have obvious effects on the bulk waves. Compared with the results in the case of neglecting the porosity-moduli relation, the results in the case of considering the porosity-moduli relation are more reasonable. The results in the case of considering the porosity-moduli relation can be degenerated into the results of elastic solid and pure fluid, while the results in the case of neglecting the porosity-moduli relation cannot be degenerated into the results of elastic solid and pure fluid. Therefore, the porosity-moduli relation must be considered in the parametric study for a certain porous medium.

Key words

frequency porosity Poisson’s ratio compressibility of solid grain porosity-moduli relation 

Chinese Library Classification

TU435 

2010 Mathematics Subject Classification

74J10 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Yi, T. H., Li, H. N., and Gu, M. Effect of different construction materials on propagation of GPS monitoring signals. Measurement, 45, 1126–1139 (2012)CrossRefGoogle Scholar
  2. [2]
    Yi, T. H., Li, H. N., and Zhao, X. Y. Noise smoothing for structural vibration test signals using an improved wavelet thresholding technique. Sensors, 12, 11205–11220 (2012)CrossRefGoogle Scholar
  3. [3]
    De Boer, R. and Liu, Z. F. Propagation of acceleration waves in incompressible saturated porous solids. Transport in Porous Media, 21, 163–173 (1995)CrossRefGoogle Scholar
  4. [4]
    Yang, J. A note on Rayleigh wave velocity in saturated soils with compressible constituents. Canadian Geotechnical Journal, 38, 1360–1365 (2001)CrossRefGoogle Scholar
  5. [5]
    Kumar, R. and Hundal, B. S. Symmetric wave propagation in a fluid-saturated incompressible porous medium. Journal of Sound and Vibration, 288, 363–373 (2005)CrossRefGoogle Scholar
  6. [6]
    Kumar, R. and Hundal, B. S. Surface wave propagation in a fluid-saturated incompressible porous medium. Sadhana, 32, 155–166 (2007)zbMATHCrossRefGoogle Scholar
  7. [7]
    Zhou, F. X., Lai, Y. M., and Song, R. X. Propagation of plane wave in non-homogeneously saturated soils. Science China Technological Sciences, 56, 430–440 (2013)CrossRefGoogle Scholar
  8. [8]
    Liu, Z. F. and de Boer, R. Dispersion and attenuation of surface waves in a fluid-saturated porous medium. Transport in Porous Media, 29, 207–223 (1997)CrossRefGoogle Scholar
  9. [9]
    Berryman, J. G. and Wang, H. F. Elastic wave propagation and attenuation in a double porosity dual-permeability medium. International Journal of Rock Mechanics and Mining Sciences, 37, 63–78 (2000)CrossRefGoogle Scholar
  10. [10]
    Dai, Z. J., Kuang, Z. B., and Zhao, S. X. Rayleigh waves in a double porosity half-space. Journal of Sound and Vibration, 298, 319–332 (2006)CrossRefGoogle Scholar
  11. [11]
    Lu, J. F., Hanyga, A., and Jeng, D. S. A linear dynamic model for a saturated porous medium. Transport in Porous Media, 68, 321–340 (2007)MathSciNetCrossRefGoogle Scholar
  12. [12]
    Nenadic, I. Z., Urban, M. W., Bernal, M., and Greenleaf, J. F. Phase velocities and attenuations of shear, Lamb, and Rayleigh waves in plate-like tissues submerged in a fluid (L). Journal of the Acoustical Society of America, 130, 3549–3552 (2011)CrossRefGoogle Scholar
  13. [13]
    Beskos, D. E., Vgenopoulou, I., and Providakis, C. P. Dynamics of saturated rocks, II: body waves. Journal of Engineering Mechanics, 115, 996–1016 (1989)CrossRefGoogle Scholar
  14. [14]
    Kim, S. H., Kim, K. J., and Blouin, S. E. Analysis of wave propagation in saturated porous media, II: parametric studies. Computer Methods in Applied Mechanics and Engineering, 191, 4075–4091 (2002)zbMATHCrossRefGoogle Scholar
  15. [15]
    Sharma, M. D. Wave propagation in a dissipative poroelastic medium. IMA Journal of Applied Mathematics, 78, 59–69 (2013)zbMATHMathSciNetCrossRefGoogle Scholar
  16. [16]
    Zhang, Y., Xu, Y. X., and Xia, J. H. Analysis of dispersion and attenuation of surface waves in poroelastic media in the exploration-seismic frequency band. Geophysical Journal International, 187, 871–888 (2011)CrossRefGoogle Scholar
  17. [17]
    Chen, W. Y., Xia, T. D., and Hu, W. T. A mixture theory analysis for the surface wave propagation in an unsaturated porous medium. International Journal of Solids and Structures, 48, 2402–2412 (2011)CrossRefGoogle Scholar
  18. [18]
    Yang, J., Wu, S. M., and Cai, Y. Q. Characteristics of propagation of elastic waves in saturated soils (in Chinese). Journal of Vibration Engineering, 9, 128–137 (1996)Google Scholar
  19. [19]
    Biot, M. A. Theory of propagation of elastic waves in a fluid-saturated porous solid. Journal of the Acoustical Society of America, 28, 168–191 (1956)MathSciNetCrossRefGoogle Scholar
  20. [20]
    Depollier, C., Allard, J. F., and Lauriks, W. Biot theory and stress-strain equations in porous sound-absorbing materials. Journal of the Acoustical Society of America, 84, 2277–2279 (1988)CrossRefGoogle Scholar
  21. [21]
    Smeulders, D. M. J., de la Rosette, J. P. M., and van Dongen, M. E. H. Waves in partially saturated porous media. Transport in Porous Media, 9, 25–37 (1992)CrossRefGoogle Scholar
  22. [22]
    Lin, C. H., Lee, V. W., and Trifunac, M. D. The reflection of plane waves in a poroelastic half-space saturated with inviscid fluid. Soil Dynamics and Earthquake Engineering, 25, 205–223 (2005)CrossRefGoogle Scholar
  23. [23]
    Luo, J. and Stevens, R. Porosity-dependence of elastic moduli and hardness of 3Y-TZP ceramics. Ceramics International, 25, 281–286 (1999)CrossRefGoogle Scholar
  24. [24]
    Tajuddin, M. Rayleigh waves in a poroelastic half-space. Journal of the Acoustical Society of America, 75, 682–684 (1984)zbMATHCrossRefGoogle Scholar
  25. [25]
    Yang, J. Rayleigh surface waves in an idealised partially saturated. Géotechnique, 55, 409–414 (2005)CrossRefGoogle Scholar
  26. [26]
    Zhang, Y., Xu, Y. X., Xia, J. H., Zhang, S. X., and Ping, P. On effective characteristic of Rayleigh surface wave propagation. Soil Dynamics and Earthquake Engineering, 57, 94–103 (2014)CrossRefGoogle Scholar
  27. [27]
    Singh, B. Reflection of plane waves from a free surface of a porothermoelastic solid half-space. Journal of Porous Media, 16, 945–957 (2013)CrossRefGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Zhijun Liu
    • 1
  • Tangdai Xia
    • 1
    Email author
  • Qingqing Zheng
    • 1
  • Weiyun Chen
    • 2
  1. 1.Research Center of Costal and Urban Geotechnical EngineeringZhejiang UniversityHangzhouChina
  2. 2.Institute of Geotechnical EngineeringNanjing Tech UniversityNanjingChina

Personalised recommendations