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Attenuation in sand: an exploratory study on the small-strain behavior and the influence of moisture condensation

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Abstract

The loss mechanisms responsible for the observed attenuation in soils are often unclear and controversial. This is particularly the case with the small-strain damping D min in air-dry sands. Ultimately, physical explanations must accommodate the observed effects of confinement, strain level, frequency, and load repetition. Three hypotheses are explored herein: measurement bias, thermoelastic relaxation, and adsorbed layers. Micro and macro-scale experimentation using photoelasticity, thermal infrared imaging, atomic force microscopy and resonant column testing are complemented with conceptual analyses. Results show that Mindlin-contact friction cannot explain the observed response of the small-strain damping ratio D min and thermoelastic loss is suggested. While thermoelastic relaxation is inherently frequency dependent, the superposition of multiple internal scales in soils can justify the observed low dependency on frequency. Moisture condensation leads to adsorbed water layers on grain surfaces, which has a small but observable effect on shear modulus and a significant influence on damping ratio. Participating loss mechanisms at small-strains may involve distortion and motion of adsorbed layers and hydration force hysteresis. Hysteretic capillary breakage at contacting asperities gains relevance when the strain exceeds the elastic threshold strain; this strain coincides with the strain range when frictional losses begin to dominate. Finally, the damping ratio in air-dry sands is very small, and causality-based attenuation–dispersion relations predict modulus dispersion about 1% per log cycle, therefore the medium can be considered non-dispersive for practical purposes.

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References

  1. Andersland O. and Ladanyi B. (2004). Frozen Ground Engineering, 2nd edn. Wiley in cooperation with ASCE Press, New York

    Google Scholar 

  2. Anderson A.L. and Hampton L.D. (1980). Acoustics of gas-bearing sediments. I. Background. J. Acoust. Soc. Am. 67(5): 1865–1889

    Article  ADS  Google Scholar 

  3. Anderson A.L. and Hampton L.D. (1980). Acoustics of gas-bearing sediments. II. Measurements and models. J. Acoust. Soc. Am. 67(5): 1890–1903

    Article  ADS  Google Scholar 

  4. Armstrong B.H. (1980). Frequency-independent background internal friction in heterogeneous solids. Geophysics 45(5): 1042–1054

    Article  ADS  Google Scholar 

  5. Armstrong B.H. (1984). Model for thermoelastic attenuation of waves in heterogeneous solids. Geophysics 49(6): 1032–1040

    Article  ADS  Google Scholar 

  6. Avramidis A.S. and Saxena S.K. (1990). The modified stiffened Drnevich resonant column apparatus. Jpn Soc. Soil Mech. Foundation Eng. 30(3): 53–68

    Google Scholar 

  7. Bhushan B., Israelachvili J.N. and Landman U. (1995). Nanotribology: friction, wear and lubrication at the atomic scale. Nature 374(13): 607–616

    Article  ADS  Google Scholar 

  8. Binggeli M. and Mate. C.M. (1994). Influence of capillary condensation of water on nanotribology studied by force microscopy. Appl. Phys. Lett. 65: 415–417

    Article  ADS  Google Scholar 

  9. Biot M.A. (1956). The theory of propagation of elastic waves in a fluid-saturated solid. I. Lower frequency range. J. Acoust. Soc. Am. 28: 168–178

    Article  MathSciNet  ADS  Google Scholar 

  10. Biot M.A. (1956). The theory of propagation of elastic waves in a fluid-saturated solid. II. Higher frequency range. J. Acoust. Soc. Am. 28: 179–191

    Article  MathSciNet  ADS  Google Scholar 

  11. Bocquet L., Charlaix E., Ciliberto S. and Crassous J. (1998). Moisture-induced ageing in granular media and the kinetics of capillary condensation. Nature 396: 735–737

    Article  ADS  Google Scholar 

  12. Bolton, M.D., Wilson, J.N.: Soil stiffness and damping. In: Krätzig, et al. (eds.) Structural Dynamics: Proceedings of the European Conference on Structural Dynamics, Eurodyn ’90, pp. 209–216. Balkema, Rotterdam (1990)

  13. Bourbié T., Coussy O. and Zinszner B. (1987). Acoustics of Porous Media. Gulf Publishing Co., Houston

    Google Scholar 

  14. Brunauer S., Emmett P.H. and Teller E. (1938). Adsorption of gases in multimolecular layers. J. Am. Chem. Soc. 60: 309–319

    Article  ADS  Google Scholar 

  15. Cascante G, Santamarina J.C. and Yassir N. (1998). Flexural excitation in a standard torsional-resonant column device. Can. Geotech. J. 35: 478–490

    Article  Google Scholar 

  16. Cascante G. and Santamarina J.C. (1996). Interparticle contact behavior and wave propagation. J. Geotech. Geoenviron. Eng. 122: 831–839

    Google Scholar 

  17. Cascante G. and Stantamarina J.C. (1997). Low strain measurements using random noise excitation. Geotech. Testing J. 20(1): 29–39

    Article  Google Scholar 

  18. Cascante G., Vanderkooy J. and Chung W. (2003). Difference between current and voltage measurement in resonant-column testing. Can. Geotech. J. 40: 806–820

    Article  Google Scholar 

  19. Cho G.C. and Santamarina J.C. (2001). Unsaturated particulate materials-particle-level studies. J. Geotech. Geoenviron. Eng. 127: 84–96

    Article  Google Scholar 

  20. Clark V.A., Tittmann B.R. and Spencer T.W. (1980). Effect of volatiles on attenuation (Q−1) and velocity in sedimentary rocks. J. Geophys. Res. 85: 5190–5198

    ADS  Google Scholar 

  21. Clifford J. (1975). Properties of water in capillaries and thin film. In: Franks, F. (eds) Water-A Comprehensive Treatise, vol 5, pp 75–132. Plenum Press, New York

    Google Scholar 

  22. Clough R.W. and Penzien J. (1993). Dynamics of Structures, 2nd edn. McGraw-Hill Inc., New York

    Google Scholar 

  23. Dini D. and Nowell. D. (2003). Prediction slip zone friction coefficient in flat and rounded contact. Wear 254: 363–369

    Article  Google Scholar 

  24. Dobry, R., Vucetic, M.: Dynamic properties and seismic response of soft clay deposits. In: Mendoza, M., Montanez, L. (eds.) Proceedings of the International Symposium on Geotechnical Engineering of Soft Soils, Mexico City, vol. 2, pp. 51–87 (1987)

  25. Dobry, R., Ladd, R.S., Yokel, F.Y., Chung, R.M., Powell, D.: Prediction of Pore Water Pressure Buildup and Liquefaction of Sands during Earthquakes by the Cyclic Strain Method. (National Bureau of Standards Building Science Series 138, U.S. Government Printing Office, Washington (1982))

  26. Ellis E.A., Soga K., Bransby M.F. and Sato M. (2000). Resonant column testing of sands with different viscosity pore fluids. J. Geotech. Geoenviron. Eng. 126(1): 10–17

    Article  Google Scholar 

  27. Fratta, D.: Passive and Active Measurements of Unique Phenomena in Geotechnical Engineering. PhD Thesis, Georgia Institute of Technology, USA (1999)

  28. Frocht M.M. (1941). Photoelasticity. Wiley, New York

    Google Scholar 

  29. García-Rojo R. and Herrmann H.J. (2005). Shakedown of unbound granular material. Granular Matter 7: 109–118

    Article  MATH  Google Scholar 

  30. Gudehus G. (2006). Seismo-hypoplasticity with a granular temperature. Granular Matter 8: 93–102

    Article  MATH  Google Scholar 

  31. Hardin B.O. and Drnevich V.P. (1972). Shear modulus and damping in soils: measurement and parameter effects. J. Soil Mech. Foundation Eng. 98: 603–624

    Google Scholar 

  32. Hardin B.O. (1965). The nature of damping in sands. J. Soil Mech. Foundation Division ASCE 91: 63–97

    Google Scholar 

  33. Hartmann U. (1994). Fundamental and special applications of non-contact scanning force microscopy. Adv. Electron. Electro Phys. 87: 79–200

    Google Scholar 

  34. Homola A.M., Israelachvili J.N., Gee M.L. and Mcguiggan P.M. (1989). Measurements of and relation between the adhesion and friction of two surfaces separated by molecularly thin liquid films. J. Tribol. Trans. ASME 111(4): 675–682

    Article  Google Scholar 

  35. Hu J., Xiao X.D., Ogletree D.F. and Salmeron M. (1995). Atomic scale friction and wear of mica. Surface Sci. 327: 358–370

    Article  ADS  Google Scholar 

  36. Ishihara K. (1996). Soil Behavior in Earthquake Geotechnics. Oxford Science, Oxford

    Google Scholar 

  37. Israelachvili J. (1991). Intermolecular and Surface Forces, 2nd edn. Academic, New York

    Google Scholar 

  38. Israelachvili J. and Wennerström H. (1996). Role of hydration and water structure in biological and colloidal interactions. Nature 379: 219–225

    Article  ADS  Google Scholar 

  39. Johnson K.L. (1961). Energy dissipation at spherical surfaces in contact transmitting oscillating forces. J. Mech. Eng. Sci. 3(4): 362–368

    Article  ADS  Google Scholar 

  40. Johnson K.L. (1984). Contact Mechanics. Cambridge University Press, New York

    Google Scholar 

  41. Johnston, D.H.: Attenuation: a state-of-the-art summary. In: Toksöz, M.N., Johnson, D.H (eds.) Seismic Wave Attenuation, pp. 123–135. SEG Geophysics Reprint Series (1981)

  42. Kim, D.S., Stokoe, K.H., Hudson, W.R.: Deformational Characteristics of Soils at Small to Intermediate Strains from Cyclic Tests. Report 1177-3. (Center for Transportation Research, Bureau of Engineering Research, the University of Texas Austin, 1991)

  43. Kjartansson E. (1979). Constant Q—wave propagation and attenuation. J. Geophys. Res. 84(B9): 4737–4748

    ADS  Google Scholar 

  44. Klimentos K. (1995). Attenuation of P- and S-waves as a method of distinguishing gas and condensate from oil and water. Geophysics 60: 447–458

    Article  ADS  Google Scholar 

  45. Knight R. and Dvorkin J. (1992). Seismic and electrical properties of sandstones at low saturations. J. Geophys. Res. 97(B12): 17425–17432

    ADS  Google Scholar 

  46. Kokusho, T.: Cyclic triaxial test of dynamic soil properties for wide strain range soils and foundations 20, 45–60 (1980)

  47. Kramer S.L. (1996). Geotechnical Earthquake Engineering. Prentice Hall, New Jersey

    Google Scholar 

  48. Landman U., Luedtke W.D. and Gao J.P. (1996). Atomic-scale issues in tribology: interfacial junctions and nano-elastohydrodynamics. Langmuir 12: 4514–4528

    Article  Google Scholar 

  49. Latham G., Ewing M., Dorman J., Press F., Tokoz N., Sutton G., Meissner R., Duennebier F., Nakamura Y., Kovach R. and Yates M. (1970). Reports: seismic data from man-made impacts on the moon. Science 170: 620–626

    Article  ADS  Google Scholar 

  50. Lazan B.J. (1968). Damping of Materials and Members in Structural Mechanics. Pergamon Press, New York

    Google Scholar 

  51. Li W.L. and Yang X.S. (1998). Effects of vibration history on modulus and damping of dry sand. J. Geotech. Geoenviron. Eng. 124(11): 1071–1081

    Article  Google Scholar 

  52. Li X.S., Yang W.L., Shen C.K. and Wang W.C. (1998). Energy-injecting virtual mass resonant column system. J. Geotech. Geoenviron. Eng. 124: 428–438

    Article  Google Scholar 

  53. Liu H.P., Anderson D.L. and Kanamori H. (1976). Velocity dispersion due to anelasticity; implications for seismology and mantle composition. Geophys. J. R. Astron. Soc. 47: 41–58

    Google Scholar 

  54. Mavko G. and Nur A. (1975). Melt squirt in the asthenosphere. J. Geophys. Res. 80(11): 1444–1448

    ADS  Google Scholar 

  55. Mavko G. and Nur A. (1979). Wave attenuation in partially saturated rocks. Geophysics 44(2): 161–178

    Article  ADS  Google Scholar 

  56. Mavko G., Kjartansson E. and Winkler K. (1979). Seismic wave attenuation in rocks. Rev. Geophys. Space Phys. 17(5): 1155–1164

    ADS  Google Scholar 

  57. Meng J. and Rix G.J. (2003). Reduction of equipment-generated damping in resonant column measurements. Géotechnique 53(4): 503–512

    Article  Google Scholar 

  58. Meyer E. and Heinzelmann H. (1992). Scanning force microscopy (SFM). In: Wiesendanger, R. and Güntherodt, H.J. (eds) Scanning Tunneling Microscopy II., pp 99–149. Springer-Verlag, Berlin

    Google Scholar 

  59. Murphy III W.F., Winkler K.W., and Klinberg R.L. (1984). Frame modulus reduction in sedimentary rocks: the effect of adsorption on grain contacts. Geophys. Res. Lett. 1(9): 805–808

    ADS  Google Scholar 

  60. Murphy III W.F., Winkler K.W., and Kleinberg R.L. (1986). Acoustic relaxation in sedimentary rocks: dependence on grain contacts and fluid saturation. Geophysics 51: 757–766

    Article  ADS  Google Scholar 

  61. Murphy III W.F. (1982). Effects of partial water saturation on attenuation in Massilon sandstone and Vycor porous glass. J. Acoust. Soc. Am. 71(5): 1458–1468

    Article  ADS  Google Scholar 

  62. Nowick A.S. and Berry B.S. (1972). Anelastic Relaxation in Crystalline Solids. Academic, New York

    Google Scholar 

  63. O’Connell R.J. and Budiansky B. (1977). Viscoelastic properties of fluid-saturated cracked solids. J. Geophys. Res. 82(36): 5719–5735

    ADS  Google Scholar 

  64. Parks G.A. (1984). Surface and interfacial free energies of quartz. J. Geophys. Res. 89(B6): 3997–4008

    ADS  Google Scholar 

  65. Persson B.N.J. (2000). Sliding Friction, Physical Principles and Applications, 2nd edn. Springer, New York

    MATH  Google Scholar 

  66. Radjai F., Wolf D.E., Jean M. and Moreau J.J. (1998). Biomodal character of stress transmission in granular packing. Phys. Rev. Lett. 80(1): 61–64

    Article  ADS  Google Scholar 

  67. Richart F.E. Jr, Hall J.R., and Woods R.D. (1970). Vibrations of Soils and Foundations. Prentice-Hall Inc., Englewood Cliffs

    Google Scholar 

  68. Santamarina J.C. and Cascante G. (1996). Stress anisotropy and wave propagation: a micromechanical view. Can. Geotech. J. 33(4): 770–782

    Google Scholar 

  69. Santamarina J.C., Klein K.A. and Fam M.A. (2001). Soils and Waves. Wiley, New York

    Google Scholar 

  70. Savage J.C. (1965). Attenuation of elastic waves in granular mediums. J. Geophys. Res. 70(16): 3935–3942

    ADS  Google Scholar 

  71. Sedin D. and Rowlen K.L. (2000). Adhesion forces measured by atomic force microscopy in humid air. Anal. Chem. 72(10): 2183–2189

    Article  Google Scholar 

  72. Spencer J.W. (1981). Stress relaxations at low frequencies in fluid- saturated rocks: attenuation and modulus dispersion. J. Geophys. Res. 86: 1803–1812

    ADS  Google Scholar 

  73. Thundat T., Zheng X.Y., Chen G.Y. and Warmack R.J. (1993). Role of relative humidity in atomic force microscopy imaging. Surface Sci. Lett. 294: L939–L943

    Google Scholar 

  74. Tittmann B.R. (1977). Lunar rock seismic Q in 3000–5000 range achieved in laboratory. Phil. Trans. R. Soc. Lond. A 285: 475–479

    Article  ADS  Google Scholar 

  75. Tittmann, B.R., Abdel-Gawad, M., Housley, R.M.: Elastic velocity and Q measurements on Apollo 12, 14, and 15 rocks. In: Proc. Lunar Sci. Conf. 3rd, pp. 2565–2575. MIT Press, Cambridge (1972)

  76. Tittmann B.R., Clark V.A., Richardson J.M. and Spencer T.W. (1980). Possible mechanism for seismic attenuation in rocks containing small amounts of volatiles. J. Geophys.l Res. 85(B10): 5199–5208

    ADS  Google Scholar 

  77. Toll J.S. (1956). Causality and the dispersion relation: logical foundations. Phys. Rev. 104(5): 1760–1770

    Article  ADS  MathSciNet  Google Scholar 

  78. Vucetic M. and Dobry R. (1991). Effect of soil plasticity on cyclic response. J. Geotech. Eng. 117(1): 89–107

    Google Scholar 

  79. Vucetic M. (1994). Cyclic threshold shear strains in soils. J. Geotech. Eng. 120(12): 2208–2227

    Article  Google Scholar 

  80. Wang, Y.H.: Attenuation in Soils and Non-linear Dynamic Effects. PhD Thesis, Georgia Institute of Technology, USA (2001)

  81. Wang Y.H., Cascante G. and Santamarina J.C. (2003). Resonant column testing: the inherent counter emf effect. ASTM Geotech. Testing J. 26(3): 342–352

    Google Scholar 

  82. Weisenhorn A.L., Hansma P.K., Albrecht T.R. and Quate C.F. (1989). Forces in atomic force microscopy in air and water. Appl. Physics Letter 54(26): 2651–2653

    Article  ADS  Google Scholar 

  83. White J.E. (1975). Computed seismic speeds and attenuation in rocks with partial gas saturation. Geophysics 40: 224–232

    Article  ADS  Google Scholar 

  84. Winkler, K.W., Murphy III, W.F.: Acoustic Velocity and Attenuation in Porous Rocks. In: Ahrens, T.J. (ed.) Rock Physics & Phase Relations—A Handbook of Physical Constants. AGU Reference Shelf 3, pp. 20–34 (1995)

  85. Winkler K., Nur A. and Gladwin M. (1979). Friction and seismic attenuation in rocks. Nature 227: 528–531

    Article  ADS  Google Scholar 

  86. Winkler K.W. and Nur A. (1982). Seismic attenuation: effects of pore fluids and frictional sliding. Geophysics 47(1): 1–15

    Article  ADS  Google Scholar 

  87. Xiao X. and Qian L. (2000). Investigation of humidity-dependent capillary force. Langmuir 16: 8153–8158

    Article  Google Scholar 

  88. Xu L., Lio A., Hu J., Ogletree D.F. and Salmeron M. (1998). Wetting and capillary phenomena of water on mica. J. Phys. Chem. B 102: 540–548

    Article  Google Scholar 

  89. Yoshizawa H., Chen Y.L. and Israelachvili J. (1993). Fundamental mechanisms of interfacial friction. J. Phys. Chem. 97: 4128–4140

    Article  Google Scholar 

  90. Zener C. (1948). Elasticity and Anelasticity of Metals. The University of Chicago Press, Chicago

    Google Scholar 

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  1. Department of Civil Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

    Y.-H. Wang

  2. Department of Civil and Environmental Engineering, Georgia Institute of Technology, 790 Atlantic Drive, Atlanta, GA, 30332, USA

    J. C. Santamarina

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Wang, YH., Santamarina, J.C. Attenuation in sand: an exploratory study on the small-strain behavior and the influence of moisture condensation. Granular Matter 9, 365–376 (2007). https://doi.org/10.1007/s10035-007-0050-6

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