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One-dimensional test problems for dynamic consolidation

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Abstract

Closed-form solutions are presented for some one-dimensional problems involving the dynamic response of saturated porous media. These solutions are useful for validating finite element codes for dynamic consolidation of soil. While they consider only elasticity and small strains, they do allow a check on the concurrent wave transmission and consolidation processes.

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Fig. 1
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Fig. 3
Fig. 4

Notes

  1. The minor oscillations in the plotted solution are simply an artifice of the numerical algorithm used to invert the Laplace transforms and are not physically real.

  2. For convenience, the results in Figs. 3 and 4 were computed using the finite difference approach, rather than Laplace transforms. This explains the slight numerical “overshoot” when a wave arrives. It should also be noted that the Talbot method of inversion of the Laplace transforms proved to be problematic for times greater than about 0.0008 s at x = 0.2 m, presumably due to singularities in the transform of pore water pressure. It is curious that this occurred at about the time the first reflected wave arrived at x = 0.2 m. This issue requires further investigation, but is beyond the scope of the present note.

References

  1. Biot MA (1956) Theory of propagation of elastic waves in a fluid-saturated porous solid. J Acoust Soc Am 28:168–191

    Article  MathSciNet  Google Scholar 

  2. Josselin De, de Jong G (1956) Wat gebeurt er in de grond tijdens het heien? De Ingenieur 68:B77–B88

    Google Scholar 

  3. Talbot A (1979) The accurate numerical inversion of Laplace transforms. J Inst Math Appl 23:97–120

    Article  MATH  MathSciNet  Google Scholar 

  4. Verruijt A (2010) An introduction to soil dynamics. Springer, Dordrecht 433

    Book  Google Scholar 

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Acknowledgments

The work described in this paper has received financial support from the Australian Research Council, through its Discovery Grant program and its Centre of Excellence in Geotechnical Science and Engineering. This support is gratefully acknowledged.

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Authors and Affiliations

  1. ARC Centre of Excellence for Geotechnical Science and Engineering, The University of Newcastle, Newcastle, NSW, Australia

    J. P. Carter, H. Sabetamal, M. Nazem & S. W. Sloan

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  1. J. P. Carter
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  2. H. Sabetamal
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  3. M. Nazem
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  4. S. W. Sloan
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Correspondence to H. Sabetamal.

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Carter, J.P., Sabetamal, H., Nazem, M. et al. One-dimensional test problems for dynamic consolidation. Acta Geotech. 10, 173–178 (2015). https://doi.org/10.1007/s11440-014-0336-x

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  • DOI: https://doi.org/10.1007/s11440-014-0336-x

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