Single-scattering approximations for coefficients in Biot's equations of poroelasticity

Journal of the Acoustical Society of America

Volumn 91, Issue 2, 1992, Pages 551-571

  Berryman, James G ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIOMATERIAL;

ARTICLE; ELASTICITY; LIQUID; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; SOLID;

EID: 0026736716     PISSN: 00014966     EISSN: NA     Source Type: Journal    
DOI: 10.1121/1.402518     Document Type: Article

References (63)

1. Avellaneda, M. (1987). “Iterated homogenization, differential effective medium theory and applications, “ Commun. Pure Appl. Math. 40, 527-554.
2. Berryman, J. G. (1980). “Long-wavelength propagation in composite elastic media I. Spherical inclusions and II. Ellipsoidal inclusions, “ J. Acoust. Soc. Am. 68, 1809-1831.
3. Berryman, J. G. (1982). “Effective medium theory for elastic composites, “ in Elastic Wave Scattering and Propagation, edited by V. K. Varadan and V. V. Varadan (Ann Arbor Science, Ann Arbor, MI), pp. 111-129.
4. Berryman, J. G. (1983). “Effective conductivity by fluid analogy for a porous insulator filled with a conductor, “ Phys. Rev. B 27, 7789-7792.
5. Berryman, J. G. (1985). “Scattering by a spherical inhomogeneity in a fluid-saturated porous medium, “ J. Math. Phys. 26, 1408-1419.
6. Berryman, J. G. (1986). “Effective medium approximation for elastic constants of porous solids with microscopic heterogeneity, “ J. Appl. Phys. 59, 1136-1140.
7. Berryman, J. G., and Milton, G. W. (1988). “Microgeometry of random composites and porous media, “ J. Phys. D: Appl. Phys. 21, 87-94.
8. Berryman, J. G., and Milton, G. W. (1991). “Exact results for generalized Gassmann's equations in composite porous media with two constituents, “ Geophysics 56, (December, 1991).
9. Berryman, J. G., and Thigpen, L. (1985). “Nonlinear and semilinear dynamic poroelasticity with microstructure, “ J. Mech. Phys. Solids 33,97-116.
10. Berryman, J. G., Thigpen, L., and Chin, R. C. Y. (1988). “Bulk elastic wave propagation in partially saturated porous solids, “ J. Acoust. Soc. Am. 84, 360-373.
11. Biot, M. A. (1956). “Theory of propagation of elastic waves in a fluid-saturated porous solid I. Low-frequency range and II. Higher frequency range, “ J. Acoust. Soc. Am. 28, 168-191.
12. Biot, M. A. (1962). “Mechanics of deformation and acoustic propagation in porous media, “ J. Appl. Phys. 33, 1482-1498.
13. Biot, M. A., and Willis, D. G. (1957). “The elastic coefficients of the theory of consolidation, “ J. Appl. Mech. 24, 594-601.
14. Brown, R. J. S. (1980). “Connection between formation factor for electrical resistivity and fluid-solid coupling factor in Biot's equations for acoustic waves in fluid-filled porous media, “ Geophysics 45, 1269-1275.
15. Brown, R. J. S., and Korringa, J. (1975). “On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid, “ Geophysics 40, 608-616.
16. Bruggeman, D. A. G. (1935). “Berechnung verschiedener physikalischer konstanten von heterogenen Substanzen I. Dielektrizittskonstanten und leitfhigkeiten der mischkrper aus isotropen Substanzen, “ Ann. Phys. (Leipzig) 24, 636-679.
17. Budiansky, B. (1965). “On the elastic moduli of some heterogeneous materials, “ J. Mech. Phys. Solids 13, 223-227.
18. Cleary, M. P., Chen, I.-W., and Lee, S.-M. (1980). “Self-consistent techniques for heterogeneous media, “ ASCE J. Eng. Mech. 106, 861-887.
19. Elliott, R. J., Krumhansl, J. A., and Leath, P. L. (1974). “The theory and properties of randomly disordered crystals and related physical systems, “ Rev. Mod. Phys. 46, 465-543.
20. Foldy, L. L. (1945). “The multiple scattering of waves I. General theory of isotropic scattering by randomly distributed scatterers, “ Phys. Rev. 67, 107-119.
21. Gassmann, F. (1951). “ber die elastizitt porser medien, “ Viertel-jahrsschr. Naturforsch. Ges. Zrich 96, 1-23.
22. Geertsma, J. (1957). “The effect of fluid pressure decline on volumetric changes of porous rocks, “ Trans. AIME 210, 331-340.
23. Green, D. H., and Wang, H. F. (1986). “Fluid pressure response to un-drained compression in saturated sedimentary rock, “ Geophysics 51, 948-956.
24. Gubernatis, J. E., and Krumhansl, J. A. (1975). “Macroscopic engineering properties of polycrystalline materials: Elastic properties, “ J. Appl. Phys. 46, 1875-1883.
25. Han, D., Nur, A., and Morgan, D. (1986). “Effect of porosity and clay content on wave velocity in sandstones, “ Geophysics 51, 2093-2107.
26. Hashin, Z., and Shtrikman, S. (1962). “On some variational principles in anisotropic and nonhomogeneous elasticity, “ J. Mech. Phys. Solids 10, 335-342.
27. Hashin, Z., and Shtrikman, S. (1963). “A variational approach to the elastic behavior of multiphase materials, “ J. Mech. Phys. Solids 11,127-140.
28. Hildebrand, F. B. (1956). Introduction to Numerical Analysis (McGraw-Hill, New York), p. 235.
29. Hill, R. (1963). “Elastic properties of reinforced solids: Some theoretical principles, “ J. Mech. Phys. Solids 11, 357-372.
30. Hill, R. (1965). “A self-consistent mechanics of composite materials, “ J. Mech. Phys. Solids 13, 213-222.
31. Johnson, D. L., Plona, T. J., Scala, C., Pasierb, F., and Kojima, H. (1982). “Tortuosity and acoustic slow waves, “ Phys. Rev. Lett. 49, 1840-1844.
32. Kirkpatrick, S. (1973). “Percolation and conduction, “ Rev. Mod. Phys. 45, 574-588.
33. Klimentos, T., and McCann, C. (1988). “Why is the Biot slow compres-sional wave not observed in real rocks?, “ Geophysics 53, 1605-1610.
34. Klimentos, T., and McCann, C. (1990). “Relationships among compres-sional wave attenuation, porosity, clay content, and permeability in sandstones, “ Geophysics 55, 998-1014.
35. Korringa, J. (1958). “Dispersion theory for electrons in a random lattice with applications to the electronic structure of alloys, “ J. Phys. Chem. Solids 7, 252-258.
36. Korringa, J., and Thompson, D. D. (1977). “Comment on the self-consistent imbedding approximation in the theory of elasticity of porous media, “ J. Geophys. Res. 82, 933-934.
37. Kuster, G. T., and Toksz, M. N. (1974). “Velocity and attenuation of seismic waves in two-phase media: Part I. Theoretical formulations & Part II. Experimental results, “ Geophysics 39, 587-618.
38. Landauer, R. (1952). “The electrical resistance of binary metallic mixtures, “ J. Appl. Phys. 23, 779-784.
39. Lax, M. (1951). “Multiple scattering of waves, “ Rev. Mod. Phys. 23,287-310.
40. McLaughlin, R. (1977). “A study of the differential scheme for composite materials, “ Int. J. Eng. Sci. 15, 237-244.
41. McTigue, D. F. (1986). “Thermoelastic response of fluid-saturated rock, “ J. Geophys. Res. 91, 9533-9542.
42. Milton, G. W. (1984). “Some Exotic Models in Statistical Physics, “ Ph.D. thesis, Cornell University, Ithaca, NY.
43. Milton, G. W. (1985). “The coherent potential approximation is a realizable effective medium scheme, “ Comm. Math. Phys. 99, 463-500.
44. Norris, A. N. (1985). “A differential scheme for the effective moduli of composites, “ Mech. Mat. 4, 1-16.
45. Norris, A. N., Callegari, A. J., and Sheng, P. (1985a). “A generalized differential effective medium theory, “ J. Mech. Phys. Solids 33, 525-543.
46. Norris, A. N., Sheng, P., and Callegari, A. J. (1985b). “Effective-medium theories for two-phase dielectric media, “ J. Appl. Phys. 57, 1990-1996.
47. Palciauskas, V. V., and Domenico, P. A. (1989). “Fluid pressures in deforming porous rocks, “ Water Resources Res. 25, 203-213.
48. Rice, J. R., and Cleary, M. P. (1976). “Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents, “ Rev. Geophys. Space Phys. 14, 227-241.
49. Roscoe, R. (1952). “The viscosity of suspensions of rigid spheres, “ Br. J. Appl. Phys. 3, 267-269.
50. Sen, P. N., Scala, C., and Cohen, M. H. (1981). “A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads, “ Geophysics 46, 781-795.
51. Sheng, P. (1990). “Effective-medium theory of sedimentary rocks, “ Phys. Rev. B 41, 4507-4512.
52. Sheng, P. (1991). “Consistent modeling of the electrical and elastic properties of sedimentary rocks, “ Geophysics 56, 1236-1243.
53. Sheng, P., and Callegari, A. J. (1984). “Differential effective medium theory of sedimentary rocks, “ Appl. Phys. Lett. 44, 738-740.
54. Soven, P. (1967). “Coherent-potential model of substitutional disordered alloys, “ Phys. Rev. 156, 809-813.
55. Taylor, D. W. (1967). “Vibrational properties of imperfect crystals with large defect concentrations, “ Phys. Rev. 156, 1017-1029.
56. Thigpen, L., and Berryman, J. G. (1985). “Mechanics of porous elastic materials containing multiphase fluid, “ Int. J. Eng. Sci. 23, 1203-1214.
57. Velicky, B., Kirkpatrick, S., and Ehrenreich, H. (1968). “Single-site approximations in the electronic theory of simple binary alloys, “ Phys. Rev. 175, 747-766.
58. Watson, K. M. (1957). “Multiple scattering by quantum-mechanical systems, “ Phys. Rev. 105, 1388-1398.
59. Wood, A. W. (1957). A Textbook of Sound (Bell, London), p. 360.
60. Yamakawa, N. (1962). “Scattering and attenuation of elastic waves, “ Geophys. Mag. (Tokyo) 31, 63-103.
61. Ying, C. F., and Truell, R. (1956). “Scattering of a plane longitudinal wave by a spherical obstacle in an isotropically elastic solid, “ J. Appl. Phys. 27, 1086-1097.
62. Yonezawa, F., and Cohen, M. H. (1983). “Granular effective medium approximation, “ J. Appl. Phys. 54, 2895-2899.
63. Zimmerman, R. W., Somerton, W. H., and King, M. S. (1986). “Compressibility of porous rocks, “ J. Geophys. Res. 91, 12 765-12 777.