High-Gradient Modeling for Love Wave Propagation in Geological Materials
Publication: Journal of Engineering Mechanics
Volume 124, Issue 12
Abstract
Based on a microstructural approach, geological material, owing to its discrete nature, can be represented by an equivalent continuum of the high-gradient type. The high-gradient continuum differs from the perfectly elastic continuum by having a characteristic length scale that is an intrinsic property of the material. Using the high-gradient stress-strain relationship, we formulate a fourth-order wave equation to describe the propagation of a Love-wave in a two-layer medium. We employ Hamilton's principle to derive the additional boundary conditions involved in the differential equation. The differential equation is then solved to study the effects of characteristic length on the wave propagation in geological material. Comparisons are made between the predicted and observed wave velocities in a two-layer geological medium during an earthquake.
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References
1.
Bathrust, R. J., and Rothenberg, L.(1988). “Micromechanical aspects of isotropic granular assemblies with linear contact interactions.”J. Appl. Mech., 55, 17–23.
2.
Bazant, Z. P., and Pijaudier-Cabot, G.(1987). “Nonlocal continuum damage localization, instability and convergence.”J. Appl. Mech., 55, 659–673.
3.
Beran, M. J., and McCoy, J. J.(1970). “The use of the strain gradient theory for analysis of random media.”Int. J. Solids and Struct., 6, 1267–1275.
4.
Born, M., and Huang, K. (1954). Dynamic theory of crystal lattice. Clarendon Press, Oxford, U.K.
5.
Chang, C. S. (1988). Micromechanical modeling of constitutive relations for granular material, M. Stake and J. T. Tenkins, eds., Elsevier, Amsterdam, The Netherlands, 271–279.
6.
Chang, C. S., and Gao, J.(1995a). “Second gradient constitutive theory for granular material with random packing structure.”Int. J. Solids and Struct., 32(16), 2279–2293.
7.
Chang, C. S., and Gao, J.(1995b). “Nonlinear dispersion of plane wave in granular media.”Int. J. Non-Linear Mech., 30(2), 111–128.
8.
Chang, C. S., and Liao, C.(1990). “Constitutive relations for particulate medium with the effect of particle rotation.”Int. J. Solids and Struct., 26(4), 437–453.
9.
Chang, C. S., and Ma, L.(1992). “Elastic material for constants for isotropic granular solids with particle rotation.”Int. J. Solids and Struct., 29(8), 1001–1018.
10.
Deresiewicz, H. (1958). “Mechanics of granular matter.”Advances in Mech., 233–306.
11.
Duffy, J., and Mindlin, R. D.(1957). “Stress-strain relations and vibrations of a granular media.”J. Appl. Mech., 24, 593–595.
12.
Eringen, A.(1972). “Linear theory of non-local elasticity and dispersion of plane waves.”Lett. Appl. Sci., 1, 129–146.
13.
Ewing, W. E., Jardetzky, W. S., and Press, F. (1957). Elastic waves in layered media. McGraw-Hill, New York.
14.
Gassman, F.(1951). “Elastic waves through a packing of spheres.”Geophys., 16, 673–685.
15.
Jeffreys, H.(1935). “The surface wave of earthquakes.”Monthly Notices Roy. Astron. Soc. (Geophys. Suppl.), London, 3(3), 336–350.
16.
Jenkins, J. T. (1988). “Volume change in small strain axisymmetric deformations of a granular material.”Micromechanics of granular materials, M. Satake and J. T. Jenkins, eds., Elsevier, Amsterdam, The Netherlands, 143–152.
17.
Love, A. E. H.(1903). “The propagation of wave motion in an isotropic elastic solid medium.”Proc., London Math. Soc., 2, 291–344.
18.
Mindlin, R. D.(1965). “Second gradient of strain and surface-tension in linear elasticity.”Int. J. Solids and Struct., 1(4), 417–438.
19.
Nowinski, J. L.(1984). “On the non-local aspects of the propagation of Love waves.”Int. J. Engrg. Sci., 22(4), 383–392.
20.
Toupin, R. A., and Gazis, D. C. (1964). “Surface effects and initial stress in continuum and lattice models of elastic crystals.”Proc., Int. Conf. on Lattice Dynamics, Pergamon Press, Tarrytown, N.Y., 594–602.
21.
Walton, K.(1987). “The effective elastic moduli of a random packing of spheres.”J. Mech. and Phys. of Solids, 35, 213–226.
22.
Wilson, J. T.(1940). “The Love waves of the south Atlantic earthquake of August 28, 1933.”Bull. Seismological Soc. of Am., 30, 273–301.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 124 • Issue 12 • December 1998
Pages: 1354 - 1359
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Dec 1, 1998
Published in print: Dec 1998
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