Skip to main content

Green’s Function for Axisymmetric Poroelasticity and Coupled Thermoelasticity

  • Chapter
Boundary Element Technology VII
  • 470 Accesses

Abstract

This paper derives Green’s functions of a ring source in an infinite poroelastic (or analogously, a. coupled thermoelastic) medium. The starting point of the solution is the axisymmetric source solution for the diffusion equation by Wrobel and Brebbia. The poroelastic solutions are found through formulae similar to those for a thermoelastic potential. The solutions are presented in both a mathematically rigorous and a computationally efficient series form.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Biot, M.A., “General theory of three-dimensional consolidation”, J. Appl. Phys., 12, 155–164, 1941.

    Article  MATH  Google Scholar 

  2. Cheng, A.H-D. and Liggett, J.A., “Boundary integral equation method for linear porous-elasticity with applications to soil consolidation,” Int. J. Numer. Meth. Eng., 20, 255–278, 1984.

    Article  MATH  Google Scholar 

  3. Detournay, E. and Cheng, A.H-D., “Poroelastic solution of a plane strain point displacement discontinuity”, J. A.pl. Mech., ASME, 54, 783–787, 1987.

    Article  MATH  Google Scholar 

  4. Cheng, A.H-D. and Predeleanu, M., “Transient boundary element formulation for poroelasticity”, Appl. M.th. Modelling, 11, 285–290, 1987.

    MathSciNet  MATH  Google Scholar 

  5. Cheng, A.H-D. and Detournay, E., “A direct boundary element method for plane strain poroelasticity”, Int. J. Numer. Anal. Meth. Geomech., 12, 551–572, 1988.

    Article  MATH  Google Scholar 

  6. Vandamme, L., Detournay, E. and Cheng, A.H-D., “A two-dimensional poroelastic displacement discontinuity method for hydraulic fracture simulation,” Int. J. Numer. A.al. Meth. Geomech, 13, 215–224, 1989.

    Article  Google Scholar 

  7. Badmus, T., Cheng, A.H-D. and Grilli, S., “A Laplace-transform based three-dimensional BEM for poroelasticity,” to appear in Int. J. Numer. Meth. Eng., 1992.

    Google Scholar 

  8. Detournay, E. and Cheng, A.H-D., “Fundamentals of poroelasticity,” to appear as Chapter 5 in Comprehensive Rock Engineering: Principles, Practice & Projects, 2, ed. J.A. Hudson, Pergamon Press, 1992.

    Google Scholar 

  9. Nowacki, W., Thermoelasticity, 2nd ed., Pergamon, London, 1986.

    Google Scholar 

  10. Biot, M.A., “Thermoelasticity and irreversible thermodynamics”, J. Appl. Phys., 27, 240–253, 1956.

    Article  MathSciNet  MATH  Google Scholar 

  11. Cheng, A.H-D., Badmus, T. and Beskos, D.E., “Integral equation for dynamic poroelasticity in frequency domain with BEM solution,” J. Eng. Medl., ASCE, 117, 1136–1157, 1991.

    Article  Google Scholar 

  12. Biot, M.A., “General solutions of the equations of elasticity and consolidation for a porous material”, J. Appl. M.ch., Trans. ASME, 78, 91–96, 1956.

    MathSciNet  Google Scholar 

  13. Wrobel, L.C. and Brebbia, C.A., “A formulation of the boundary element method for axisymmetric transient heat conduction”, Int. J. Heat Mass Transfer, 24, 843–850, 1981.

    Article  MATH  Google Scholar 

  14. Lennon, G.P., Liu, P.L-F. and Liggett, J.A., “Boundary integral equation solution to axisymmetric potential flows, 1. Basic formulation”, Water Resour. Res., 15, 1102–1106, 1979.

    Google Scholar 

  15. Abramowitz, M. and Stegun, I.A., Handbook of Mathematical Functions, Dover, 1972.

    Google Scholar 

  16. Gradshteyn, I.S. and Ryzhik, I.M., Table of Integrals, Series, and Products, Academic Press, 1980.

    Google Scholar 

  17. Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T., “Numerical Recipes”, Cambridge University Press, 1986.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Computational Mechanics Publications

About this chapter

Cite this chapter

Cheng, A.HD., Cui, L. (1992). Green’s Function for Axisymmetric Poroelasticity and Coupled Thermoelasticity. In: Brebbia, C.A., Ingber, M.S. (eds) Boundary Element Technology VII. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2872-8_6

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-2872-8_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-85166-782-6

  • Online ISBN: 978-94-011-2872-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics