Acta Mechanica Solida Sinica

, Volume 27, Issue 1, pp 41–53 | Cite as

Acoustoelastic Theory for Fluid-Saturated Porous Media

Article

Abstract

Based on the finite deformation theory of the continuum and poroelastic theory, the acoustoelastic theory for fluid-saturated porous media (FSPM) in natural and initial coordinates is developed to investigate the influence of effective stresses and fluid pore pressure on wave velocities. Firstly, the assumption of a small dynamic motion superimposed on a largely static pre-deformation of the FSPM yields natural, initial, and final configurations, whose displacements, strains, and stresses of the solid-skeleton and the fluid in an FSPM particle could be described in natural and initial coordinates, respectively. Secondly, the subtraction of initial-state equations of equilibrium from the final-state equations of motion and the introduction of non-linear constitutive relations of the FSPM lead to equations of motion for the small dynamic motion. Thirdly, the consideration of homogeneous pre-deformation and the plane harmonic form of the small dynamic motion gives an acoustoelastic equation, which provides analytical formulations for the relation of the fast longitudinal wave, the fast shear wave, the slow shear wave, and the slow longitudinal wave with solid-skeleton stresses and fluid pore-pressure. Lastly, an isotropic FSPM under the close-pore jacketed condition, open-pore jacketed condition, traditional unjacketed condition, and triaxial condition is taken as an example to discuss the velocities of the fast and slow shear waves propagating along the direction of one of the initial principal solid-skeleton strains. The detailed discussion shows that the wave velocities of the FSPM are usually influenced by the effective stresses and the fluid pore pressure. The fluid pore-pressure has little effect on the wave velocities of the FSPM only when the components of the applied initial principal solid-skeleton stresses or strains are equal, which is consistent with the previous experimental results.

Key Words

acoustoelasticity fluid-saturated porous media wave velocity the effective stress fluid pore pressure 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Crampin, S. and Chastin, S., A review of shear wave splitting in the crack-critical crust. Geophysical Journal International, 2003, 155(1): 221–240.CrossRefGoogle Scholar
  2. 2.
    Crampin, S. and Peacock, S., A review of shear-wave splitting in the compliant crack-critical anisotropic Earth. Wave Motion, 2005, 41(1): 59–77.CrossRefGoogle Scholar
  3. 3.
    Coussy, O., Poromechanics. West Sussex: John Wiley & Sons Inc, 2004.MATHGoogle Scholar
  4. 4.
    Coussy, O., Mechanics and physics of porous solids. West Sussex: John Wiley & Sons Inc., 2010.CrossRefGoogle Scholar
  5. 5.
    Biot, M., General theory of three-dimensional consolidation. Journal of Applied Physics, 1941, 12(2): 155–164.CrossRefGoogle Scholar
  6. 6.
    Biot, M., General solutions of the equations of elasticity and consolidation for a porous material. Journal of Applied Mechanics, 1956, 23(1): 91–96.MathSciNetMATHGoogle Scholar
  7. 7.
    Biot, M., Theory of deformation of a porous viscoelastic anisotropic solid. Journal of Applied Physics, 1956, 27(5): 459–467.MathSciNetCrossRefGoogle Scholar
  8. 8.
    Berryman, J.G., Confirmation of Biot’s theory. Applied Physics Letters, 1980, 37(4): 382–384.CrossRefGoogle Scholar
  9. 9.
    Plona, T.J., Observation of a second bulk compressional wave in a porous media at ultrasonic frequency. Applied Physics Letters, 1980, 36: 259–261.CrossRefGoogle Scholar
  10. 10.
    Carcione, J.M., Morency, C. and Santos, J.E., Computational poroelasticity — A review. Geophysics, 2010, 75(5): 75A299–75A243.CrossRefGoogle Scholar
  11. 11.
    Sgard, F., Castel, F. and Atalla, N., Use of a hybrid adaptive finite element/modal approach to assess the sound absorption of porous materials with meso-heterogeneities. Applied Acoustics, 2011, 72(4): 157–168.CrossRefGoogle Scholar
  12. 12.
    Puente, D.L., Josep, Dumbser, M., Kser, M. and Igel, H., Discontinuous Galerkin methods for wave propagation in poroelastic media. Geophysics, 2008, 73(5): T77–T97.CrossRefGoogle Scholar
  13. 13.
    Niu, F., Silver, P.G., Daley, T.M., Cheng, X. and Majer, E.L., Preseismic velocity changes observed from active source monitoring at the Parkfield SAFOD drill site. Nature, 2008, 454(7201): 204–208.CrossRefGoogle Scholar
  14. 14.
    Johnson, P.A. and Rasolofosaon, P.N.J., Nonlinear elasticity and stress-induced anisotropy in rock. Journal of Geophysical Research, 1996, 101(B2): 3113–3124.CrossRefGoogle Scholar
  15. 15.
    Tian, J.Y. and Wang, E.F., Ultrasonic method for measuring in-situ stress based on acoustoelasticity theory. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(supp.2): 3719–3724.MathSciNetGoogle Scholar
  16. 16.
    Pao, Y., Sachse, W. and Fukuoka, H., Acoustoelastic and Ultrasonic Measurement of Residual Stress. Orlando: Academic Press, 1984.Google Scholar
  17. 17.
    Nakata, N. and Snieder, R., Near-surface weakening in Japan after the 2011 Tohoku-Oki earthquake. Geophysical Research Letters, 2011, 38(17): L17302.CrossRefGoogle Scholar
  18. 18.
    Cheng, X., Niu, F. and Wang, B., Coseismic velocity change in the rupture zone of the 2008 Mw 7.9 Wenchuan earthquake observed from ambient seismic noise. Bulletin of the Seismological Society of America, 2010, 100(5B): 2539–2550.CrossRefGoogle Scholar
  19. 19.
    Wang, B., Zhu, P., Chen, Y., Niu, F. and Wang, B., Continuous subsurface velocity measurement with coda wave interferometry. Journal of Geophysical Research, 2008, 113(B12): B12313.CrossRefGoogle Scholar
  20. 20.
    Sens-Schönfelder, C. and Wegler, U., Passive image interferometry and seasonal variations of seismic velocities at Merapi Volcano, Indonesia. Geophysical Research Letters, 2006, 33(21): L21302.CrossRefGoogle Scholar
  21. 21.
    Lu, L. and Yan, G.J., Formation temperature and pressure with the influence on seismic wave velocity. Marine Geology Letters, 2005, 21(9): 13–16.Google Scholar
  22. 22.
    Wang, Z., Fundamentals of seismic rock physics. Geophysics, 2001, 66(2): 398–412.CrossRefGoogle Scholar
  23. 23.
    Sayers, C.M., Geophysics under stress: mechanical applications of seismic and borehole acoustic waves: 2010 distinguished instructor short course. 13, Tulsa: Society of Exploration Geophysicists, 2010.Google Scholar
  24. 24.
    Tosaya, C.A., Acoustical Properties of Clay-bearing Rocks. Ph.D. Thesis, Stanford University, 1982.Google Scholar
  25. 25.
    Stanchits, S., Lockner, D. and Zinke, J., Shear wave splitting in foliated rock. 2011, http://earthquake.usgs.gov/research/physics/lab/shearwave.php.
  26. 26.
    Biot, M.A., Theory of stability and consolidation of a porous medium under initial stress. Journal of Mathematics and Mechanics, 1963, 12(4): 521–542.MathSciNetMATHGoogle Scholar
  27. 27.
    Grinfeld, M. and Norris, A., Acoustoelasticity theory and applications for fluid-saturated porous media. The Journal of the Acoustical Society of America, 1996, 100(3): 1368–1374.CrossRefGoogle Scholar
  28. 28.
    Sharma, M.D., Effect of initial stress on the propagation of plane waves in a general anisotropic poroelastic medium. Journal of Geophysical Research, 2005, 110(B11): B11307.CrossRefGoogle Scholar
  29. 29.
    Chattaraj, R., Samal, S.K. and Mahanti, N.C., Propagation of torsional surface wave in anisotropic poroelastic medium under initial stress. Wave Motion, 2011, 48(2): 184–195.MathSciNetCrossRefGoogle Scholar
  30. 30.
    He, L.F. and Liu, J., Acoustoelasticity Technology. Beijing: Science press, 2002.Google Scholar
  31. 31.
    Biot, M.A., Mechanics of deformation and acoustic propagation in porous media. Journal of Applied Physics, 1962, 33(4): 1482–1498.MathSciNetCrossRefGoogle Scholar
  32. 32.
    Biot, M.A., Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range. The Journal of the Acoustical Society of America, 1956, 28(2): 168–178.MathSciNetCrossRefGoogle Scholar
  33. 33.
    Biot, M.A. and Willis, D.G., The elastic coefficients of the theory of consolidation. Journal of Applied Mechanics, 1957, 24: 594–601.MathSciNetGoogle Scholar
  34. 34.
    Dutta, N.C. and Koestler, A.G., Pressure prediction from seismic data: implications for seal distribution and hydrocarbon exploration and exploitation in the deepwater Gulf Of Mexico, Norwegian Petroleum Society Special Publications: Elsevier, 1997: 187–199.Google Scholar
  35. 35.
    Boer, L.D.D., Sayers, C.M., Nagy, Z.R., Hooyman, P.J. and Woodward, M.J., Pore pressure prediction using well-conditioned seismic velocities. First Break, 2006, 24(5): 43–50.Google Scholar
  36. 36.
    Zhang, R.Z., Guo, L.C. and Xu, H., Review pore pressure earthquake prediction technology. Progress in Exploration Geophysics, 2005, 28(2): 90–96.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2014

Authors and Affiliations

  1. 1.Institute of Crustal DynamicsChina Earthquake AdministrationBeijingChina

Personalised recommendations