Skip to main content
Log in

Solution of a Green’s function for a saturated porous medium in a half-space subjected to a torsional force

  • Published:
Earthquake Engineering and Engineering Vibration Aims and scope Submit manuscript

Abstract

Based on the solutions of the Green’s function for a saturated porous medium obtained by the authors, and using transformation of axisymmetric coordinates, Sommerfeld integrals and superposition of the influence field on a free surface, the authors have obtained displacement solutions of a saturated porous medium subjected to a torsional force in a half-space. The relationship curves of the displacement solutions and various parameters (permeability, frequency, etc.) under action of a unit of torque are also given in this paper. The results are consistent with previous Reissner’s solutions, where a two-phase medium decays to a single-phase medium. The solution is useful in solving relevant dynamic problems of a two-phase saturated medium in engineering.

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

Access this article

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

  • AASHO (2000), Standard Specification for Highway Materials and Methods of Sampling and Testing, American Association of State Highway Officials, Washington.

    Google Scholar 

  • Biot MA (1956), “Theory of Elastic Wave in a Fluid-Saturated Porous Solid, I. Low-frequency Range,” J. Acoust. Soc. Am., 28(1): 168–178.

    Article  Google Scholar 

  • Biot MA (1962), “Mechanics of Deformation and Acoustic Propagation in Porous Media,” J. Appl. Phys., 33(4): 1482–1498.

    Article  Google Scholar 

  • Burridge and Vagas CA (1979), “The fundamental Solution in Dynamic Poroselasticity,” Geophysical Journal of the Royal Astronomic Society, 58(1): 61–90.

    Article  Google Scholar 

  • Ding BY, Fan LB and Wu JH (2000), “A Solution for Displacement Field of Point Source of Concentrated Force in Saturated Two-phase Medium and Its Application,” Chinese J. Geophys, 43(1): 141–148.

    Google Scholar 

  • Ding BY and Yuan JH (2011), “Dynamic Green’s Functions of a Two-phase Saturated Medium Subjected to Concentrated Force,” Int. J. Solid Struct., 48: 2288–2303.

    Article  Google Scholar 

  • Ding BY, Yuan JH and Pan XD (2008), “The Abstracted and Integrated Green Functions and OOP of BEM in Soil Dynamics,” Science in China Series G, 51(12): 1926–1937.

    Article  Google Scholar 

  • Ewing, GH and Jardetzky WS (1957), Elastic Waves in Layered Media, McGraw-Hill Company, New York, 222–285.

  • Pal PC (2001), “Effect of Dynamic Visco-elasticity on Vertical and Torsional Vibrations of a Half-space,” Sadhana, 26: 371–377.

    Article  Google Scholar 

  • Philippaopoulos AJ (1987), “Waves in a Partially Saturated Layered Half-space: Analytic Formulation.” Bull. Seismol. Soc. Am., 77(5): 1838–1853.

    Google Scholar 

  • Philippaopoulos AJ (1988a), “Lamb’s Problem for Fhud-saturated Porous Media,” Bull. Seismol. Soc. Am., 78(2): 908–923.

    Google Scholar 

  • Philippaopoulos AJ (1988b), “Wave in Partially Saturated Medium due to Surface Loads,” J. Engr. Mech., ASCE, 114(10): 1740–1759.

    Article  Google Scholar 

  • Rahman M (1998), “The Reissner-Sagoci Problem for a Half-space under Buried Torsional Forces,” Int. J. Solid Struct., 37: 1119–1132.

    Article  Google Scholar 

  • Reissner E (1937), “Freie und Erzwungene Torsionsschwingungen des elastischen halbraumes,” Ingenieur-Arehiv, 8: 229–245.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Boyang Ding.

Additional information

Supported by: National Natural Science Foundation of China Under Grant No. 11172268

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ding, B., Chen, J. & Ouyang, M. Solution of a Green’s function for a saturated porous medium in a half-space subjected to a torsional force. Earthq. Eng. Eng. Vib. 11, 133–138 (2012). https://doi.org/10.1007/s11803-012-0104-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11803-012-0104-6

Keywords

Navigation