Buried Point Source in a Poroelastic Half-Space
Publication: Journal of Engineering Mechanics
Volume 123, Issue 8
Abstract
The problem under consideration is to determine the motion of a poroelastic half-space produced by a buried point source with arbitrary time variation. The method followed is to generate the associated Green's functions as a superposition of the singular solution corresponding to the inhomogeneous problem for the whole space plus a contribution representing relevant effects due to the presence of the free surface. The mathematical approach is based on integral transform techniques: Fourier transform with respect to the time and Hankel transform with respect to the space. The Green's functions for the displacement fields (solid and pore fluid motion respectively) show additional integratable singularities arising from Rayleigh poles and by eight branch points resulting from combinations of three radicals containing the three fundamental wave numbers of poroelastic propagation. Recognizing that the branch points and poles are complex valued as a result of dissipation by the skeletal frame as well as viscous dissipation due to the relative motion of the pore fluid with respect to the frame material, integration in the ω-k domain is done along a path that coincides with the real wave-number axis. Such integration is required only for surface contributions to the Green's function. The motion generated by a point source in the poroelastic half-space at an observation distance is synthesized by three direct waves radiating from the source (fast/slow dilatational and a transverse wave) and by a series of waves (nine for the general case) associated with reflections at the free surface (P1P1, P1S, SP1, etc.). The present integral solution gives an idea of the format of an eigenfunction synthesis through expansion of the two vector fields (for the solid and fluid phases) in terms of Hensen eigenvectors. It is shown that the solutions presented in this study reduce to known counterparts of elastodynamics for zero porosity and, in particular, to the classical solution by Pekeris. Finally, the Green's functions for a point source buried in a poroelastic half-space complement those obtained in a recent study for the case of a line source.
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Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 123 • Issue 8 • August 1997
Pages: 860 - 869
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Aug 1, 1997
Published in print: Aug 1997
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