Analytical and Experimental Studies on Biot Flow–Induced Damping in Saturated Soil Specimens in Resonant Column Tests
Publication: International Journal of Geomechanics
Volume 17, Issue 8
Abstract
This paper presents an analytical and experimental investigation of Biot flow–induced damping in saturated soil specimens in resonant column tests. In the analytical investigation, the solid skeleton is treated as poroviscoelastic (i.e., equivalent linear). Biot flow–induced damping is evaluated based on the half-power bandwidth and free vibration decay methods. These solutions are found to be generally consistent with a closed-form analytical solution readily available in the literature. The solutions indicate that maximum values of Biot flow–induced damping occur in coarse sand and gravel, and can be practically neglected for less permeable soils (e.g., fine sand, silt, and clay). The solutions also indicate that Biot flow–induced damping increases as porosity increases, and decreases considerably as the ratio of the mass polar moment of inertia of the loading system to the specimen increases. In the experimental investigation, resonant column tests were conducted on granular specimens in dry and saturated conditions to quantify Biot flow–induced damping and compare with the analytical solutions. The test results are found to be in general agreement with the analytical solutions within the measurement accuracy of the device used in this study.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The analytical study and resonant column tests conducted in this study were supported by the U.S. National Science Foundation (Grants CMMI-0826097 and CMMI-1059588). This support is gratefully acknowledged.
References
ASTM. (2007). “Standard test methods for modulus and damping of soils by resonant column method.” D4015-07, West Conshohocken, PA.
ASTM. (2014). “Standard test methods for specific gravity of soil solids by water pycnometer.” D854-14, West Conshohocken, PA.
Bardet, J. P. (1995). “The damping of saturated poroelastic soils during steady-state vibrations.” Appl. Math. Comput., 67(1–3), 3–31.
Biot, M. A. (1956a). “Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range.” J. Acoust. Soc. Am., 28(2), 168–178.
Biot, M. A. (1956b). “Theory of propagation of elastic waves in a fluid-saturated porous solid. ІІ. Higher frequency range.” J. Acoust. Soc. Am., 28(2), 179–191.
Biot, M. A. (1962). “Mechanics of deformation and acoustic propagation in porous media.” J. Appl. Phys., 33(4), 1482–1498.
Bishop, A. W. (1959). “The principle of effective stress.” Teknisk Ukeblad, 106(39), 859–863.
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, Netherlands, 209–216.
Cascante, G., Vanderkooy, J., and Chung, W. (2005). “A new mathematical model for resonant column measurements including eddy-current effects.” Can. Geotech. J., 42(1), 121–135.
Darendeli, M. B. (2001). “Development of a new family of normalized modulus reduction and material damping curves.” Ph.D. dissertation, Civil Engineering, Univ. of Texas, Austin, TX.
Das, B. M. (2010). Principles of geotechnical engineering, 7th Ed., Cengage Learning, Stamford, CT.
Dvorkin, J., and Nur, A. (1993). “Dynamic poroelasticity: A unified model with the squirt and the Biot mechanisms.” Geophys., 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, 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., 10–17.
Gajo, A. (1996). “The effects of inertial coupling in the interpretation of dynamic soil tests.” Géotechnique, 46(2), 245–257.
Gajo, A., and Mongiovi, L. (1995). “An analytical solution for the transient response of saturated linear elastic porous media.” Int. J. Numer. Anal. Methods Geomech., 19(6), 399–413.
Garg, S. K., Nayfeh, A. H., and Good, A. J. (1974). “Compressional waves in fluid-saturated elastic porous media.” J. Appl. Phys., 45(5), 1968–1974.
Hall, J. R. (1962). “Effect of amplitude on damping and wave propagation in granular materials.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Univ. of Florida, Gainesville, FL.
Hall, J. R., and Richart, F. E. (1963). “Dissipation of elastic wave energy in granular soils.” J. Soil Mech. Found. Div., 89(6), 27–56.
Hardin, B. O. (1965). “The nature of damping in sands.” J. Soil Mech. Found. Div., 91(SM1), 63–97.
Hwang, S. K. (1997). “Investigation of the dynamic properties of natural soils.” Ph.D. dissertation, Civil Engineering, Univ. of Texas, Austin, TX.
Ishihara, K. (1996). Soil behavior in earthquake geotechnics, Oxford University Press, Oxford, UK.
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.
Kameo, Y., Adachi, T., and Hojo, M. (2008). “Transient response of fluid pressure in a poroelastic material under uniaxial cyclic loading.” J. Mech. Phys. Solids, 56(5), 1794–1805.
Kim, D. S. (1991). “Deformational characteristics of soils at small strains from cyclic tests.” Ph.D. dissertation, Civil Engineering, Univ. of Texas, Austin, TX.
Kramer, S. L. (1996). Geotechnical earthquake engineering, Prentice Hall, Upper Saddle River, NJ.
Meng, J., and Rix, G. J. (2003). “Reduction of equipment-generated damping in resonant column measurements.” Géotechniques, 53(5), 503–512.
Michaels, P. (2006). “Relating damping to soil permeability.” Int. J. Geomech., 158–165.
Michaels, P. (2008). “Water, inertial damping, and the complex shear modulus.” Proc., Geotechnical Earthquake Engineering and Soil Dynamics IV, D. Zeng, M. T. Manzari, and D. R. Hiltunen, eds., ASCE, Reston, VA, 1–10.
Phillips, C., and Hashash, Y. M. A. (2009). “Damping formulation for nonlinear 1D site response analyses.” Soil Dyn. Earthquake Eng., 29(7), 1143–1158.
Qiu, T. (2008). “Pore fluid induced damping of saturated soil in resonant column tests.” Proc., Geotechnical Earthquake Engineering and Soil Dynamics IV, D. Zeng, M. T. Manzari, and D. R. Hiltunen, eds., ASCE, Reston, VA, 1–10.
Qiu, T. (2010). “Analytical solution for Biot flow–induced damping in saturated soil during shear wave excitations.” J. Geotech. Geoenviron. Eng., 1501–1508.
Qiu, T., and Fox, P. J. (2006). “Hydraulic damping of saturated poroelastic soils during steady-state vibration.” J. Eng. Mech., 859–870.
Qiu, T., and Huang, Y. B. (2012). “Energy dissipation in nearly saturated poroviscoelastic soil column during quasi-static compressional excitations.” J. Eng. Mech., 1263–1274.
Qiu, T., Huang, Y. B., Guadalupe-Torres, Y., Baxter, C., and Fox, P. (2015). “Effective soil density for small-strain shear waves in saturated granular materials.” J. Geotech. Geoenviron. Eng., 04015036.
Santamarina, J. C., Klein, K. A., and Fam, M. A. (2001). Soils and waves: Particulate materials behavior, characterization, and process monitoring, Wiley, New York.
Sasanakul, I., and Bay, J. (2010). “Calibration of equipment damping in a resonant column and torsional shear testing device.” Geotech. Test. J., 33(5), 1–12.
Schanz, M. (2009). “Poroelastodynamics: linear models, analytical solutions, and numerical methods.” Appl. Mech. Rev., 62(3), 030803.
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.” Geophys., 46(5), 781–795.
Simon, B. R., Zienkiewicz, C., and Paul, D. K. (1984). “An analytical solution for the transient response of saturated porous elastic solids.” Int. J. Numer. Anal. Methods Geomech., 8(4), 381–398.
Stoll, R. D. (1989). “Sediment acoustics.” Lecture notes in earth sciences, 26, Springer, New York.
Stoll, R. D., and Bryan, G. M. (1970). “Wave attenuation in saturated sediments.” J. Acoust. Soc. Am., 47(5), 1440–1447.
Vucetic, M., and Dobry, R. (1991). “Effect of soil plasticity on cyclic response.” J. Geotech. Eng., 87–107.
Wang, Y., Cascante, G., and Santamarinca, C. (2003). “Resonatn column testing: The inherent counter EMF effect.” Geotech. Test. J., 26(3), 342–352.
Wei, C., and Muraleetharan, K. K. (2006). “Acoustical characterization of fluid-saturated porous media with local heterogeneities: Theory and application.” Int. J. Solids Struct., 43(5), 982–1008.
Zienkiewicz, O. C., Chan, A. H. C., Pastor, M., Schrefler, B. A., and Shiomi, T. (1999). Computational geomechanics with special reference to earthquake engineering, John Wiley & Sons, New York.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 17 • Issue 8 • August 2017
Copyright
© 2017 American Society of Civil Engineers.
History
Received: Feb 29, 2016
Accepted: Jan 17, 2017
Published online: Mar 27, 2017
Published in print: Aug 1, 2017
Discussion open until: Aug 27, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.