Skip to main content

Time-Dependent Solutions

  • Chapter
  • 600 Accesses

Abstract

This chapter presents some time-dependent solutions for cavity expansion in rock and soil. In rock mechanics, cavity solutions derived from constitutive models based on visco-elasticity and visco-plasticity have been applied to tunnel problems. As far as soil mechanics is concerned, studies have been carried out on the pore pressure changes around a driven pile and an excavated tunnel in soils. This chapter will concentrate on the solutions with applications to these two types of geotechni-cal problems.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Carslaw, H.S. and Jaeger, J.C. (1959). Conduction of Heat in Solids. Clarendon Press, Oxford.

    Google Scholar 

  • Carter, J.P.. (1988). A semi-analytical solution for swelling around a borehole. Internationaljournal for Numerical and Analytical Methods in Geomechanics, 12, 197–212.

    Article  Google Scholar 

  • Carter, J.P. and Booker, J.R. (1982). Elastic consolidation around a deep circular tunnel. International Journal of Solids and Structures, 18(12), 1059–1074.

    Article  Google Scholar 

  • Flugge, W. (1967). Viscoelasticity. Blaisdell Publishing Company, Massachusetts.

    Google Scholar 

  • Fritz, P. (1984). An analytical solution for axisymmetric tunnel problems in elasto-visco-plastic media. International Journal for Numerical and Analytical Methods in Geome-chanics, 8, 325–342.

    Article  Google Scholar 

  • Gnirk, P.F. and Johnson, R.E. (1974). The deformation behaviour of a circular mine shaft situated in a visco-elastic medium under hydrostatic stress. Proceedings of the 6th Symposium on Rock Mechanics, 231–259.

    Google Scholar 

  • Goodman, R.E. (1989). Introduction to Rock Mechanics. Chapman and Hall.

    Google Scholar 

  • Jaeger, J.C. and Cook (1976). Fundamentals of Rock Mechanics. Chapman and Hall.

    Google Scholar 

  • Ladanyi, B. (1993). Time-dependent response of rock around tunnels. In: Comprehensive Rock Engineering (Editor: J.A. Hudson), Pergamon Press, Oxford, Vol. 2, 77–112.

    Google Scholar 

  • Lee, E.H. (1955). Stress analysis in viscoelastic bodies. Quarterly Applied Mathematics, 13 (2), 183–190.

    Google Scholar 

  • Nonaka, T. (1981). A time-independent analysis for the final state of an elasto-visco-plas-tic medium with internal cavities. International Journal of Solids and Structures, 17, 961–967.

    Article  Google Scholar 

  • Randolph, M.F. and Wroth, C.P. (1979). An analytical solution for the consolidation around a driven pile. International Journal for Numerical and Analytical Methods in Geomechanics, 3, 217–229.

    Article  Google Scholar 

  • Salamon, M.D.G. (1974). Rock mechanics of underground excavations. Proceedings of the 3rd Congress of International Society of Rock Mechanics, 1(B), 994–1000.

    Google Scholar 

  • Scott, R.F. (1990). Radial consolidation of a phase-change soil. Geotechnique, 40(2), 211–221.

    Article  Google Scholar 

  • Soderberg, L.O. (1962). Consolidation theory applied to time effects. Geotechnique, 12(3), 217–225.

    Article  Google Scholar 

  • Talbot, A. (1979). The accurate numerical inversion of Laplace transforms. Journal of the Institute of Mathematical Applications, 23, 97–120.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Hai-Sui Yu

About this chapter

Cite this chapter

Yu, HS. (2000). Time-Dependent Solutions. In: Cavity Expansion Methods in Geomechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9596-4_6

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-9596-4_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4023-7

  • Online ISBN: 978-94-015-9596-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics