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On the displacements produced in a porous elastic half-space by an impulsive line load. (Non-dissipative case)

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Summary

On the basis of Biot's dynamical theory of poroelasticity the disturbance produced by an impulsive line load in a porous elastic half-space is studied. Using the Laplace-Fourier transform we have solved for the displacement potentials in terms of which the displacements and stresses in the transformed space are expressible. The expressions for the solid displacements in the interior as well as on the surface of the half-space are obtained by Cagniard's technique. The displacements are expressed in terms of six algebraic terms — three of which are identified as the disturbance due to specific wave fronts and the others represent the head wave contributions. When specialized our results agree with those for the common elastic half-space.

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References

  1. M. A. Biot (1956),Theory of Propagation of Elastic Waves in a Fluid Saturated Porous Solid, J. Acoust. Soc. Am.28, 168–191.

  2. H. Deresiewicz (1960),The Effect of Boundaries on Wave Propagation in a Liquid Filled Porous Solid: I Reflection of Plane Waves at a Free Plane Boundary (Non-Dissipative Case), Bull. Seism. Soc. Am.50, 599–607.

  3. H. Deresiewicz andJ. T. Rice (1962),The Effect of Boundaries on Wave Propagation in a Liquid Filled Porous Solid: III Reflection of Plane Waves at a Free Plane Boundary (General Case), Bull. Seism. Soc. Am.52, 595–625.

  4. D. C. Gakenheimer (1969),Transient Excitation of an Elastic Half-space by a Point Load Travelling on the Surface, Ph.D. Thesis, California Institute of Technology, Engineering Mechanics.

  5. J. P. Jones (1962),Rayleigh Waves in Porous Elastic Saturated Solid, J. Acoust. Soc. Am.33, 959–962.

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Paul, S. On the displacements produced in a porous elastic half-space by an impulsive line load. (Non-dissipative case). PAGEOPH 114, 605–614 (1976). https://doi.org/10.1007/BF00875654

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Keywords

  • Biot
  • Wave Front
  • Dynamical Theory
  • Line Load
  • Head Wave