Constitutive models for wave propagation in soils

Applied Mechanics Reviews

Volumn 59, Issue 1-6, 2006, Pages 146-174

  Bloom, Frederick ^a  

^a NORTHERN ILLINOIS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTITUTIVE MODELS; DISTRIBUTION FUNCTION MODEL; ELASTIC-PLASTIC MODELS; MULTIPHASE MODELS;

ELASTIC MODULI; MATHEMATICAL MODELS; PRESSURE EFFECTS; SOILS;

ELECTROMAGNETIC WAVE PROPAGATION;

EID: 33846375786     PISSN: 00036900     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2177685     Document Type: Review

References (72)

1. Nelson, I., Baron, M. L., and Sandler, I., 1971, "Mathematical Models for Geological Materials for Wave-Propagation Studies," Shock Waves and the Mechanical Properties of Solids, J. J. Burke and V, Weiss, eds., Syracuse University Press, Syracuse, pp. 289-331.
2. Merkle, D. H., and Dass, W. C., 1985, "Fundamental Properties of Soils for Complex Dynamic Loadings," AFOSR Report No. TR-85-1232.
3. Bloom, F., 2006, "Wave Propagation in Partially Saturated Soils," Appl. Mech. Rev., accepted for publication.
4. Kim, K., Blouin, S., Chitty, D., and Merkle, D., 1988, "Experimental and Theoretical Response of Multiphase Porous Media to Dynamic Loads," AFOSR Report No. TR-88-1004.
5. Nikolaevski, V. N., 1982, "On Static and Dynamic Response of Geomaterials," Proc. IUTAM Conference on Deformation and Failure of Granular Materials, Delft, Elsevier, Amsterdam.
6. Nikolaevski, V. N., 1971, "Governing Equations of Plastic Deformation of a Granular Medium," I. Appl. Math. Mech., 35, pp. 1019-1029.
7. Nikolaevski, V. N., Syrnikov, N., and Shefter, G., 1975, "Dynamics of Elasto-Plastic Dilatating Media," Advances in Mechanics of Solids (Nauka, Moscow, Galerkin Vol.), pp. 397-413.
8. Houlsby, G. T., 1993, "Interpretation of Dilation as a Kinematical Constraint," Modern Approaches to Plasticity, D. Kolymbus, ed., Elsevier, New York, pp. 19-36.
9. Houlsby, G. T., 1991, "How the Dilatancy of Soils Affects Their Behavior," Proc. 10th Eur. Conf. Soil Mech. Found. Eng., Associazione Geotecnica Italiana, Florence, Italy, Vol, 4, pp. 1189-1202.
10. Kanatani, K. I., 1982, "Macroscopic and Microscopic Descriptions of the Mechanics of Granular Materials," Deformation and Failure of Granular Materials, Proc. IUTAM Conf., Delft, P. A. Vermeer and H. J. Luger, eds, Elsevier, Amsterdam, pp. 273-284.
11. Kanatani, K. I., 1982, "A Plasticity Theory for the Kinematics of Ideal Granular Materials," Int. J. Eng. Sci., 20, pp. 1-13.
12. Dass, W., Bratton, J., and Higgins, C., 1982, "Fundamental Properties of Soils for Complex Dynamic Loadings," AFOSR Report No. TR-82-0101.
13. McTigue, D. F., and Passman, S. L., 1982, "The Effective Stress Principle and Mixture Theory," preprint.
14. McTique, D. F., Wilson, R. K., and Nunziato, J. W., 1982, "An Effective Stress Principle for Partially Saturated Granular Media," Mechanics of Granular Materials: New Models and Constitutive Relations, I. T. Jenkins and M. Satake, eds., Elsevier, Amsterdam, pp. 195-210.
15. Raats, P. A. C., 1968, "Forces Acting on the Solid Phase of a Porous Medium," Z. Angew. Math. Phys., 19, pp. 606-613.
16. Kansa, E. J., 1982, "The Response of Shocks in Unsaturated Geological Media Under a Wide Range of Permeabilities," preprint, Lawrence Livermore National Laboratory.
17. Swift, R. P., and Burton, D. E., 1984, UCRL-53568, LLNL.
18. Walker, R. E., and Lofton, S., 1994, "Ground Shock Attenuation in Three Phase Earth Materials," Workshop on Constitutive Modeling of Air and Water Saturated Sand for Shock Propagation Prediction, US Naval Research Lab., Washington, DC.
19. Ahrens, T. J., 1988, "Equation of State of Earth Media," Report to the Defense Nuclear Agency, Report No. DNA-TR-88-265, Washington, DC.
20. Foster, A. N., 1977, "Fluid Wave Propagation in Saturated and Nearly Saturated Sands," Ph.D. thesis, University of Michigan.
21. Bakanova, S., 1976, "Thermodynamic Properties of Water at High Pressures and Temperatures," Sov. Phys. JETP, 41, pp. 544-571.
22. Goodman, M. A., and Cowin, S. C., 1972, "A Continuum Theory for Granular Materials," Arch. Ration. Mech. Anal., 44, pp. 249-266.
23. Cowin, S. C., 1972, "Themodynamic Model for Porous Materials With Vacuous Pores." J. Appl. Phys., 43, pp. 2495-2497.
24. Cowin, S. C., and Goodman, M, A., 1976, "A Variational Principle for Granular Materials," Z. Angew. Math. Mech., 56, pp. 281-286.
25. Nunziato, J. W., and Walsh, E. K., 1977, "On the Influence of Void Compaction and Material Non-Uniformity on the Propagation of One-Dimensional Acceleration Waves in Granular Materials," Arch. Ration. Mech. Anal., 64, pp. 299-316.
26. Carroll, M. M., and Holt, A. C., 1972, "Static and Dynamic Pore-Collapse Relations for Ductile Porous Materials," J. Appl. Phys., 43, pp. 1626-1636.
27. Nunziato, J. W., and Walsh, E. K., 1977, "Small-Amplitude Wave Behavior in One-Dimensional Granular Solids," ASME J. Appl. Mech., 44, pp. 559-564.
28. Nunziato, J. W., and Walsh, E. K., 1978, "One-Dimensional Shock Waves in Uniformly Distributed Granular Materials," Int. J. Solids Struct., 14, pp. 681-689.
29. Cowin, S. C., and Nunziato, J. W., 1981, "Waves of Dilatancy in a Granular Material With Incompressible Granules," Int. J. Eng. Sci., 19, pp. 993-1008.
30. Nunziato, J. W., and Herrmann, W., 1972, "The General Theory of Shock Waves in Elastic Nonconductors," Arch. Ration. Mech. Anal., 47, pp. 272-287.
31. Chen, P. J., and Gurtin, M. E., 1971, "The Growth of One-Dimensional Shock Waves in Elastic Nonconductors," Int. J. Solids Struct., 7, pp. 5-10.
32. Nunziato, J. W., and Yarrington, P., 1977, "A Continuum Theory of Porous Materials With Applications to Wave Propagation Calculations," Symposium on Applications of Computer Methods in Engineering, University of Southern California, L. C. Welford, ed.
33. Hermann, W., 1965, "Constitutive Equation for the Dynamic Compaction of Ductile Porous Materials," J. Appl. Phys., 40, pp. 2490-2499.
34. Butcher, B. M., 1971, "The Description of Strain-Rate Effects in Shocked Porous Materials," Shock Waves and the Mechanical Properties of Solids, J. J. Burke and V. Weiss, eds., Syracuse University Press, Syracuse, pp. 227-244.
35. Drucker, D. C., and Prager, W., 1952, "Soil Mechanics and Plastic Analysis of Limit Design," Q. Appl. Math., 10, pp. 157-165.
36. Grigorian, S S., 1980, "On Basic Notions of Soil Dynamics," (in Russian), Prikl. Mat. Mekh., 24, pp. 6-23.
37. Kaliski, S., and Osiecka, J., 1951, "Unloading Wave for a Body With Rigid Unloading Characteristics," Proc. Vib. Probl. 1, pp. 1-17.
38. Nowacki, W. K., 1978, Stress Waves in Non-Elastic Solids, Pergamon Press, London.
39. Lyakhov, G. M., 1959, "Shock Waves in Multicomponent Media," Izv. Akad. Nauk SSSR. Otd. Tekh. Nauk, Metall. Topl., 1.
40. Lyakhov, G. M., 1974, Principles of the Dynamics of Detonation Waves in Soils and Rocks, Nedra, Moscow.
41. Rakhmatulin, K. A., 1969, "Wave Propagation in Multicomponent Media," Prikl. Mat. Mekh., 33, pp. 598-601.
42. Lyakhov, G. M., and Okhitin, V. N., 1974, "Spherical Explosion Waves in Multicomponent Media," Prikl. Mekh. Tekh. Fiz., 2, pp. 75-84.
43. Krivtsov, V. A., 1974, "Equation of the Compression of Water-Saturated Sand and the Limit of its Applicability," Prikl. Mekh. Tekh. Fiz., 4, pp. 576-579.
44. Nowacki, W. K., and Raniecki, B., 1987, "Theoretical Analysis of Dynamic Compacting of Soil Around a Spherical Source of Explosion," Arch. Mech., 39, pp. 359-384.
45. Wlodarczyk, E., 1987, "Concentrated Explosion in Water Saturated Soil, Part I. Analytic Solution of the Problem," J. Tech. Phys., 28, pp. 221-241.
46. Nowacki, W. K., and Guelin, P., 1993, "Dynamic Compacting of Soils," Modern Approaches to Plasticity, D. Kolymbas, ed., Elsevier, New York, pp. 671-689.
47. Guelin, P., and Nowacki, W. K., 1992, "Stress Waves in Elastic-Plastic Solids With Discrete Memory," J. Tech. Phys., 33, pp. 167-204.
48. Mandel, J., 1974, Introduction à la Mécanique des Milieux Continus Déformables, PWN, Warsaw.
49. Reynolds, O., 1885, "On the Dilatancy of Media Composed of Rigid Particles in Contact," Philos. Mag., 5, pp. 469-481.
50. Rodionov, V. N., Adushkin, V. V., Kostuchenko, V. N., Nikolaevski, V. N., Romashov, A. N., and Zvetkov, V. M., 1971, Mechanical Effects of Underground Explosions, Nedra, Moscow.
51. Ziegler, H., 1977, An Introduction to Thermomechanics, North-Holland. Amsterdam.
52. Kanatani, K. L, 1982, "Macroscopic and Microscopic Descriptions of the Mechanics of Granular Materials," Deformation and Failure of Granular Materials, Proc. IUTAM Conf., Delft, P. A. Vermeer and H. J. Luger, eds., Elsevier, Amsterdam, pp. 273-284.
53. Kanatani, K. I., 1982, "Dilatant Plastic Deformation of Granular Materials.'' Int. J. Eng. Sci., 20, pp. 879-884.
54. Truesdell, C., and Noll, W., 1965, "The Nonlinear Field Theories of Mechanics," Handbuch der Physik III/3, Springer-Verlag, Berlin.
55. Drucker, D. C., 1953, "Limit Analysis of Two and Three Dimensional Soil Mechanics Problems," J. Mech. Phys. Solids, 1, pp. 217-226.
56. Roscoe, K. H., Shofield, A. N., and Wroth, C. P.. 1958, "On the Yielding of Soils," Geotechnique, 8, pp. 22-53.
57. Nemat-Nasser, S., and Shokooh, A., 1980, "On Finite Plastic Flows of Compressible Materials With Internal Friction." Int. J. Solids Struct., 16. pp. 495-514.
58. Goodman, M. A., and Cowin, S. C., 1972, "A Continuum Theory for Granular Materials," Arch. Ration. Mech. Anal., 44, pp. 249-266.
59. Corapcioglu, M. Y., 1989, "Wave Propagation in Porous Media: A Review," Transport Processes in Porous Media, J. Bear and M. Y. Corapcioglu, eds., Reidel, Dordrecht.
60. Biot, M. A., 1941, "General Theory of Three-Dimensional Consolidation," J. Appl. Phys., 12, pp. 155-164.
61. Biot, M. A. 1956, "Theory of Propagation of Elastic Waves in u Fluid-Saturated Porous Solid," J. Acoust. Soc. Am., 28, pp. 168-191.
62. Ogushwitz, P. K., 1985, "Applicability of the Biot Theory: I. Low Porosity Materials, II. Suspensions, III. Wave Speeds Versus Depth in Marine Sediments," J. Acoust. Soc. Am., 77, pp. 429-464.
63. Stoll, R. D., 1977, "Acoustic Waves in Ocean Sediments," Geophysics, 42. pp. 751-725.
64. Stoll, R. D., and Bryan, G. M., 1970, "Wave Attenuation in Saturated Sediments," J. Acoust. Soc. Am., 47, pp. 1440-1447.
65. Bear, J., 1972, Dynamics of Fluids in Porous Media, Elsevier, New York.
66. Bear, J., and Bachmat, Y., 1984, "Transport Pheomena in Porous Media-Basic Equations," Fundamentals of Transport Pheonomena in Porous Media, J. Bear and M. Y. Corapcioglu, eds., Martinus Nijhoff, Dordrecht, pp. 3-61.
67. Verruijt, A., 1984, "The Theory of Consolidation, Fundamentals of Transport Phenomena in Porous Media," I. Bear and M. Y. Corapcioglu, eds., Martinas Nijhoff, Dordrecht, pp. 349-368.
68. Zienkiewicz, O. D., and Bettess, P., 1982, "Soils and Other Saturated Media Under Transient, Dynamic Conditions: General Formulation, and the Validity of Various Simplifying Assumptions," Soil Mechanics, Transient and Cyclic Loads, G. N. Pande and O. C. Zienkiewicz, eds., Wiley, New York, pp. 1-16.
69. Brinkman, A. C., 1948, "On the Permeability of Media Consisting of Closely Packed Porous Particles," Appl. Sci. Res., Sect. A. 1, pp. 81-86.
70. Ishihara, K., 1965, "Theory of Consolidation of a Porous Material With Heat Effect Based on the Irreversible Thermodynamics." Trans. Jpn. Soc. Civ. Eng., 113, 28-42.
71. Nagumo, S., 1965, "Effect of Pore Structure for Deformation and Failure of Porous Media," Bull. Earthquake Res. Inst., Univ. Tokyo, 43.
72. Biot, M. A., 1956, "Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid," J. Acoust. Soc. Am., 28, pp. 168-178.