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TECHNICAL PAPERS

Dynamic Analysis of a One-Dimensional Poroviscoelastic Column

[+] Author and Article Information
M. Schanz

Institute of Applied Mechanics, Technical University Braunschweig, D-38023 Braunschweig, Germany

A. H.-D. Cheng

Department of Civil and Environmental Engineering, University of Delaware, Newark, DE 19716

J. Appl. Mech 68(2), 192-198 (Jul 01, 2000) (7 pages) doi:10.1115/1.1349416 History: Received December 12, 1999; Revised July 01, 2000
Copyright © 2001 by ASME
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References

Biot,  M. A., 1941, “General Theory of Three-Dimensional Consolidation,” J. Appl. Phys., 12, pp. 155–164.
Biot,  M. A., 1955, “Theory of Elasticity and Consolidation for a Porous Anisotropic Solid,” J. Appl. Phys., 26, pp. 182–185.
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, No. 2, pp. 168–191.
Detournay, E., and Cheng, A. H.-D., 1993, Fundamentals of Poroelasticity, Vol. II (Comprehensive Rock Engineering: Principles, Practice & Projects), Pergamon Press, Tarrytown, NY, Chapter 5, pp. 113–171.
Biot,  M. A., 1956, “Theory of Deformation of a Porous Viscoelastic Anisotropic Solid,” J. Appl. Phys., 27, No. 5, pp. 459–467.
Wilson,  R. K., and Aifantis,  E. C., 1982, “On the Theory of Consolidation With Double Porosity,” Int. J. Eng. Sci., 20, pp. 1009–1035.
Vgenopoulou,  I., and Beskos,  D. E., 1992, “Dynamic Behavior of Saturated Poroviscoelastic Media,” Acta Mech., 95, pp. 185–195.
Abousleiman,  Y., Cheng,  A. H.-D., Jiang,  C., and Roegiers,  J.-C., 1996, “Poroviscoelastic Analysis of Borehole and Cylinder Problems,” Acta Mech., 109, No. 1–4, pp. 199–219.
Schanz,  M., and Cheng,  A. H.-D., 2000, “Transient Wave Propagation in a One-Dimensional Poroelastic Column,” Acta Mech., 145, No. 1-4, pp. 1–8.
Lubich,  C., 1988, “Convolution Quadrature and Discretized Operational Calculus. I.,” Numer. Math., 52, pp. 129–145.
Narayanan,  G. V., and Beskos,  D. E., 1982, “Numerical Operational Methods for Time-Dependent Linear Problems,” Int. J. Numer. Methods Eng., 18, pp. 1829–1854.
Cheng,  A. H.-D., Sidauruk,  P., and Abousleiman,  Y., 1994, “Approximate Inversion of the Laplace Transform,” Mathematica J. 4, No. 2, pp. 76–82.
Schanz,  M., and Antes,  H., 1997, “Application of ‘Operational Quadrature Methods’ in Time Domain Boundary Element Methods,” Meccanica, 32, No. 3, pp. 179–186.
Christensen, R. M., 1971, Theory of Viscoelasticity, Academic Press, New York.
Bonnet, G., and Auriault, J.-L., 1985, “Dynamics of Saturated and Deformable Porous Media: Homogenization Theory and Determination of the Solid-Liquid Coupling Coefficients,” N. Boccara and M. Daoud, eds., Physics of Finely Divided Matter, Springer-Verlag, Berlin, pp. 306–316.
Cheng,  A. H.-D., Badmus,  T., and Beskos,  D. E., 1991, “Integral Equations for Dynamic Poroelasticity in Frequency Domain With BEM Solution,” J. Eng. Mech. 117, No. 5, pp. 1136–1157.
Kim,  Y. K., and Kingsbury,  H. B., 1979, “Dynamic Characterization of Poroelastic Materials,” Exp. Mech., 19, pp. 252–258.
Badiey,  M., Cheng,  A. H.-D., and Mu,  Y., 1998, “From Geology to Geoacoustics—Evaluation of Biot-Stoll Sound Speed and Attenuation for Shallow Water Acoustics,” J. Acoust. Soc. Am., 103, No. 1, pp. 309–320.
Lubich,  C., 1988, “Convolution Quadrature and Discretized Operational Calculus. II,” Numer. Math., 52, pp. 413–425.
Schanz,  M., and Antes,  H., 1997, “A New Visco- and Elastodynamic Time Domain Boundary Element Formulation,” Comput. Mech., 20, No. 5, pp. 452–459.
Schanz,  M., 1999, “A Boundary Element Formulation in Time Domain for Viscoelastic Solids,” Commun. Numer. Meth. Eng. 15, pp. 799–809.

Figures

Grahic Jump Location
One-dimensional rheological three-parameter model
Grahic Jump Location
One-dimensional column under dynamic loading
Grahic Jump Location
Absolute value of the displacements |u⁁y(ω,y=l)| at the top of the column versus frequency ω
Grahic Jump Location
Displacements uy(t,y=l) at the top of the column versus time t
Grahic Jump Location
Pressure p(t,y=995 m) versus time: wave propagation for different values of κ in an “infinite” soil column
Grahic Jump Location
Pressure p(t,y=995 m) versus time: wave propagation for different damping cases

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