Analytical Solution for Biot Flow–Induced Damping in Saturated Soil during Shear Wave Excitations
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 136, Issue 11
Abstract
This paper presents a theoretical study of Biot flow–induced damping in saturated soil during shear wave excitations. The solid skeleton is treated as equivalent linear. Biot flow–induced damping is evaluated for the cases of resonant column tests and site response analysis, based on the spectral response of a soil column/layer under harmonic torsional/horizontal excitations. Closed-form analytical solutions indicate that Biot flow–induced damping is hydraulic conductivity and frequency dependant. At the first resonance in a resonant column test, Biot flow–induced damping is dependent on a dimensionless hydraulic conductivity parameter K. For K within the range of 0.01 to 100, corresponding to coarse sands and clean gravels, Biot flow–induced damping may have an important contribution to total soil damping, especially at small strain levels. For site response analysis, Biot flow–induced damping should be considered for coarse sands and clean gravels, but can be practically neglected for fine sands, silts, and clays. The effects of soil porosity, mass coupling, and non-Poiseuille flow on Biot flow–induced damping are discussed.
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Acknowledgments
Support of this study is provided by the U.S. National Science Foundation under Grant No. NSFCMMI-0826097. This support is gratefully acknowledged. The writer also thanks the three anonymous reviewers for their very insightful comments and suggestions.
References
Akbar, N., Mavko, G., Nur, A., and Dvorkin, J. (1994). “Seismic signatures of reservoir transport properties and pore fluid distribution.” Geophysics, 59(8), 1222–1236.
Bardet, J. P. (1992). “A viscoelastic model for the dynamic behavior of saturated poroelastic soils.” J. Appl. Mech., 59(1), 128–135.
Bardet, J. P. (1995). “The damping of saturated poroelastic soils during steady-state vibrations.” Appl. Math. Comput., 67, 3–31.
Biot, M. A. (1956). “Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range. II. Higher frequency range.” J. Acoust. Soc. Am., 28(2), 168–191.
Biot, M. A. (1962). “Mechanics of deformation and acoustic propagation in porous media.” J. Appl. Phys., 33(4), 1482–1498.
Bolton, M. D., and Wilson, J. N. (1990). “Soil stiffness and damping.” Structural dynamics, W. B. Kratzig, D. E. Beskos, and I. G. Vardoulakis, eds., Balkema, Rotterdam, The Netherlands, 209–216.
Das, B. M. (2010). Principles of geotechnical engineering, 7th Ed., Cengage Learning, Stamford, CT.
Drnevich, J. P. (1972). “Undrained cyclic shear of saturated sand.” J. Soil Mech. and Found. Div., 98(SM8), 807–825.
Dvorkin, J., and Nur, A. (1993). “Dynamic poroelasticity: A unified model with the squirt and the Biot mechanisms.” Geophysics, 58(4), 524–533.
Ellis, E. A., Soga, K., Bransby, M. F., and Sato, M. (1998). “Effect of pore fluid viscosity on the cyclic behavior of sands.” Proc., Centrifuge 98, T. Kimura, O. Kusakabe, and J. Takemura, eds., Balkema, Rotterdam, The Netherlands, 217–222.
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.
Gajo, A. (1996). “The effects of inertial coupling in the interpretation of dynamic soil tests.” Geotechnique, 46(2), 245–257.
Hall, J. R. (1962), “Effect of amplitude on damping and wave propagation in granular materials.” Ph.D. thesis, Univ. of Florida, Gainesville, FL.
Hall, J. R., and Richart, F. E. (1963). “Dissipation of elastic wave energy in granular soils.” J. Soil Mech. and Found. Div., 89(6), 27–56.
Hardin, B. O. (1965). “The nature of damping in sands.” J. Soil Mech. and Found. Div., 91(SM1), 63–97.
Johnson, D. L., Plona, T. J., Scala, C., Pasierb, F., and Kojima, H. (1982). “Tortuosity and acoustic slow waves.” Phys. Rev. Lett., 49(25), 1840–1844.
Kramer, S. L. (1996). Geotechnical earthquake engineering, Prentice-Hall, Upper Saddle River, NJ.
Mavko, G., and Nur, A. (1979). “Wave attenuation in partially saturated rocks.” Geophysics, 44(2), 161–178.
Michaels, P. (2006). “Relating damping to soil permeability.” Int. J. Geomech., 6(3), 158–165.
Michaels, P. (2008). “Water, inertial damping, and the complex shear modulus.” Geotechnical Earthquake Engineering and Soil Dynamics IV, GSP 181, ASCE, Reston, VA.
Miksis, M. J. (1988). “Effect of contact line movement on the dissipation of waves in partially saturated rocks.” J. Geophys. Res., 93(B6), 6624–6634.
Murphy, W. F., Winkler, K. W., and Kleinberg, R. L. (1986). “Acoustic relaxation in sedimentary rocks: Dependence on grain contacts and fluid saturation.” Geophysics, 51(3), 757–766.
Qiu, T. (2008). “Pore fluid induced damping of saturated soil in resonant column tests.” Geotechnical Earthquake Engineering and Soil Dynamics IV, GSP 181, ASCE, Reston, VA.
Qiu, T., and Fox, P. J. (2006). “Hydraulic damping of saturated poroelastic soils during steady-state vibration.” J. Eng. Mech., 132(8), 859–870.
Qiu, T., and Fox, P. J. (2008). “Effective soil density for propagation of small strain shear waves in saturated soil.” J. Geotech. Geoenviron. Eng., 134(12), 1815–1819.
Richart, F. E., Jr., Hall, J. R., and Woods, R. D. (1970). Vibrations of soils and foundations, Prentice-Hall, Englewood Cliffs, NJ.
Santamarina, J. C., Klein, K. A., and Fam, M. A. (2001). Soils and waves: Particulate materials behavior, characterization, and process monitoring, Wiley, New York.
Sen, P. N., Scala, C., and Cohen, J. H. (1981). “A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads.” Geophysics, 46(5), 781–795.
Stoll, R. D. (1989). “Sediment acoustics.” Lecture notes in earth sciences, Vol. 26, Springer, New York.
Stoll, R. D., and Bryan, G. M. (1970). “Wave attenuation in saturated sediments.” J. Acoust. Soc. Am., 47(5B), 1440–1447.
Vucetic, M., Lanzo, G., and Doroudian, M. (1998). “Damping at small strains in cyclic simple shear test.” J. Geotech. Geoenviron. Eng., 124(7), 585–594.
Wang, Z., and Nur, A. (1990). “Dispersion analysis of acoustic velocities in rocks.” J. Acoust. Soc. Am., 87(6), 2384–2395.
Wilson, J. M. R. (1988). “A theoretical and experimental investigation onto the dynamic behavior of soil.” Ph.D. thesis, Univ. of Cambridge, Cambridge, U.K.
Zienkiewicz, O. C., Chang, C. T., and Bettess, P. (1980). “Drained, undrained, consolidating and dynamic behavior assumptions in soils.” Geotechnique, 30(4), 385–395.
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Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 136 • Issue 11 • November 2010
Pages: 1501 - 1508
Copyright
© 2010 ASCE.
History
Received: Apr 4, 2009
Accepted: Mar 25, 2010
Published online: Mar 27, 2010
Published in print: Nov 2010
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