Skip to main content
SpringerLink
Log in

Layer-element analysis of multilayered saturated soils subject to axisymmetric vertical time-harmonic excitation

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The analytical layer-elements for a single poroelastic soil layer and the underlying half-space are established using an algebraic manipulation and Hankel transform. According to the boundary conditions and adjacent continuity conditions of general stresses and displacements, a global matrix equation in the transform domain for multilayered saturated soil media is assembled and solved. Solutions in the frequency domain can be further obtained with an inverse Hankel transform. Numerical examples are used to examine accuracy of the present method and demonstrate effects of soil parameters and load conditions on dynamic responses of the multilayered poroelastic saturated soils.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Biot, M. A. General theory of three-dimensional consolidation. Journal of Applied Physics, 12, 155–164 (1941)

    Article  MATH  Google Scholar 

  2. Biot, M. A. Theory of propagation of elastic waves in a fluid-saturated porous solid I: low-frequency range. The Journal of the Acoustical Society of America, 28, 168–178 (1956)

    Article  MathSciNet  Google Scholar 

  3. Biot, M. A. Mechanics of deformation and acoustic propagation in porous media. Journal of Applied Physics, 33, 1482–1498 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  4. Paul, S. On the displacements produced in a porous elastic half-space by an impulsive line load. (non-dissipative case). Pure and Applied Geophysics, 114, 605–614 (1976)

    Article  Google Scholar 

  5. Paul, S. On the disturbance produced in a semi-infinite poroelastic medium by a surface load. Pure and Applied Geophysics, 114, 615–627 (1976)

    Article  Google Scholar 

  6. Lamb, H. On the propagation of tremors over the surface of an elastic solid. Philosophical Transactions of the Royal Society of London Series A, 203, 1–42 (1904)

    Article  MATH  Google Scholar 

  7. Gakenheimer, D. C. and Miklowitz, J. Transient excitation of an elastic half space by a point load traveling on the surface. Journal of Applied Mechanics, 36, 505–515 (1969)

    Article  MATH  Google Scholar 

  8. Halpern, M. R. and Christiano, P. Response of poroelastic halfspace to steady-state harmonic surface tractions. International Journal for Numerical and Analytical Methods in Geomechanics, 10, 609–632 (1986)

    Article  MATH  Google Scholar 

  9. Halpern, M. R. and Christiano, P. Steady-state harmonic response of a rigid plate bearing on a liquid-saturated poroelastic halfspace. Earthquake Engineering and Structural Dynamics, 14, 439–454 (1986)

    Article  Google Scholar 

  10. Philippacopoulos, A. J. Lamb’s problem for fluid-saturated, porous media. Bulletin of the Seismological Society of America, 78, 908–923 (1988)

    Google Scholar 

  11. Philippacopoulos, A. J. Axisymmetric vibration of disk resting on saturated layered half-space. Journal of Engineering Mechanics ASCE, 115, 2301–2322 (1989)

    Article  Google Scholar 

  12. Senjuntichai, T. and Rajapakse, R. Dynamic Green’s functions of homogeneous poroelastic halfplane. Journal of Engineering Mechanics ASCE, 120, 2381–2404 (1994)

    Article  Google Scholar 

  13. Rajapakse, R. K. N. D. and Senjuntichai, T. Dynamic response of a multi-layered poroelastic medium. Earthquake Engineering and Structural Dynamics, 24, 703–722 (1995)

    Article  MATH  Google Scholar 

  14. Zhang, Y. K. and Huang, Y. The non-axisymmetrical dynamic response of transversely isotropic saturated poroelastic media. Applied Mathematics and Mechanics (English Edition), 22, 63–78 (2001) DOI 10.1007/BF02437945

    Article  MATH  Google Scholar 

  15. Wang, X. G. and Huang, Y. 3-D dynamic response of transversely isotropic saturated soils. Applied Mathematics and Mechanics (English Edition), 26, 1409–1419 (2005) DOI 10.1007/BF03246246

    Article  MathSciNet  MATH  Google Scholar 

  16. Cai, Y. Q., Meng, K., and Xu, C. J. Stable response of axisymmetric two-phase water-saturated soil. Journal of Zhejiang University-Science A, 5, 1022–1027 (2004)

    Article  Google Scholar 

  17. Cai, Y. Q., Xu, C. J., Zheng, Z. F., and Wu, D. Z. Vertical vibration analysis of axisymmetric saturated soil. Applied Mathematics and Mechanics (English Edition), 27, 83–89 (2006) DOI 10.1007/s10483-006-0111-z

    Article  MATH  Google Scholar 

  18. Ding, B. Y., Dang, G. H., and Yuan, J. H. Lamb’s integral formulas of two-phase saturated medium for soil dynamic with drainage. Applied Mathematics and Mechanics (English Edition), 31, 1113–1124 (2010) DOI 10.1007/s10483-010-1347-9

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhou, S. H., He, C., and Di, H. G. Dynamic 2.5-D Green’s function for a poroelastic half-space. Engineering Analysis with Boundary Elements, 67, 96–107 (2016)

    Article  MathSciNet  Google Scholar 

  20. He, C., Zhou, S. H., Guo, P. J., Di, H. G., and Xiao, J. H. Dynamic 2.5-D Green’s function for a point fluid source in a layered poroelastic half-space. Engineering Analysis with Boundary Elements, 77, 123–137 (2017)

    Article  MathSciNet  Google Scholar 

  21. Zheng, P., Zhao, S. X., and Ding, D. Dynamic Green’s functions for a poroelastic half-space. Acta Mechanica, 224, 17–39 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  22. Zheng, P., Ding, B. Y., Zhao, S. X., and Ding, D. 3D dynamic Green’s functions in a multilayered poroelastic half-space. Applied Mathematical Modelling, 37, 10203–10219 (2013)

    Article  MathSciNet  Google Scholar 

  23. Lu, J. F. and Hanyga, A. Fundamental solution for a layered porous half space subject to a vertical point force or a point fluid source. Computation Mechanics, 35, 376–391 (2005)

    Article  MATH  Google Scholar 

  24. Liu, T. Y. and Zhao, C. B. Dynamic analyses of multilayered poroelastic media using the generalized transfer matrix method. Soil Dynamics and Earthquake Engineering, 48, 15–24 (2013)

    Article  Google Scholar 

  25. Liu, Z. X., Liang, J. W., and Wu, C. Q. Dynamic Green’s function for a three-dimensional concentrated load in the interior of a poroelastic layered half-space using a modified stiffness matrix method. Engineering Analysis with Boundary Elements, 60, 51–66 (2015)

    Article  MathSciNet  Google Scholar 

  26. Ai, Z. Y., Wang, L. J., and Zeng, K. Analytical layer-element method for 3D thermoelastic problem of layered medium around a heat source. Meccanica, 50, 49–59 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  27. Ai, Z. Y., Wang, L. J., and Li, B. Analysis of axisymmetric thermo-elastic problem in multilayered material with anisotropic thermal diffusivity. Computers and Geotechnics, 65, 80–86 (2015)

    Article  Google Scholar 

  28. Ai, Z. Y., Cheng, Y. C., and Zeng, W. Z. Analytical layer-element solution to axisymmetric consolidation of multilayered soils. Computers and Geotechnics, 38, 227–232 (2011)

    Article  Google Scholar 

  29. Ai, Z. Y. and Zeng, W. Z. Analytical layer-element method for non-axisymmetric consolidation of multilayered soils. International Journal for Numerical and Analytical Methods in Geomechanics, 36, 533–545 (2012)

    Article  Google Scholar 

  30. Ai, Z. Y. and Wang, L. J. Axisymmetric thermal consolidation of multilayered porous thermoelastic media due to a heat source. International Journal for Numerical and Analytical Methods in Geomechanics, 39, 1912–1931 (2015)

    Article  Google Scholar 

  31. Ai, Z. Y. and Wang, L. J. Three-dimensional thermo-hydro-mechanical responses of stratified saturated porothermoelastic material. Applied Mathematical Modelling, 40, 8912–8933 (2016)

    Article  MathSciNet  Google Scholar 

  32. Ai, Z. Y., Li, Z. X., and Cang, N. R. Analytical layer-element solution to axisymmetric dynamic response of transversely isotropic multilayered half-space. Soil Dynamics and Earthquake Engineering, 60, 22–30 (2014)

    Article  Google Scholar 

  33. Ai, Z. Y. and Li, Z. X. Time-harmonic response of transversely isotropic multilayered half-space in a cylindrical coordinate system. Soil Dynamics and Earthquake Engineering, 66, 69–77 (2014)

    Article  Google Scholar 

  34. Ai, Z. Y. and Zhang, Y. F. Plane strain dynamic response of a transversely isotropic multilayered half-plane. Soil Dynamics and Earthquake Engineering, 75, 211–219 (2015)

    Article  Google Scholar 

  35. Ai, Z. Y. and Ren, G. P. Dynamic analysis of a transversely isotropic multilayered half-plane subjected to a moving load. Soil Dynamics and Earthquake Engineering, 83, 162–166 (2016)

    Article  Google Scholar 

  36. Timoshenko, S. P. and Goodier, J. N. Theory of Elasticity, 3rd ed., McGraw-Hill, New York (1970)

    MATH  Google Scholar 

  37. Zienkiewicz, O. C. Basic Formulation of Static and Dynamic Behaviour of Soil and Other Porous Media, Springer, New York (1982)

    Book  MATH  Google Scholar 

  38. Sneddon, I. N. The Use of Integral Transform, McGraw-Hill, New York (1972)

    MATH  Google Scholar 

  39. Ai, Z. Y., Yue, Z. Q., Tham, L. G., and Yang, M. Extended Sneddon and Muki solutions for multilayered elastic materials. International Journal of Engineering Science, 40, 1453–1483 (2002)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geotechnical Engineering, Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, College of Civil Engineering, Tongji University, Shanghai, 200092, China

    Zhiyong Ai & Lihua Wang

Authors
  1. Zhiyong Ai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lihua Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhiyong Ai.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ai, Z., Wang, L. Layer-element analysis of multilayered saturated soils subject to axisymmetric vertical time-harmonic excitation. Appl. Math. Mech.-Engl. Ed. 38, 1295–1312 (2017). https://doi.org/10.1007/s10483-017-2241-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-017-2241-8

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation