Skip to main content

Abstract

This book is mainly concerned with analytical and semi-analytical solutions for cavity expansion problems. In practice, however, it is inevitable that numerical methods must be used and this is particularly true when more sophisticated soil models are employed. For this reason, this chapter presents the basic formulations for finite element analysis of cavity expansion problems. To validate the finite element formulations, the analytical solutions presented in previous chapters need to be used for comparison.

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 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Been, K and Jefferies, M.G. (1985). A state parameter for sands. Geotechnique, 35(2), 99–112.

    Article  Google Scholar 

  • Bolton, M. D. (1986). The strength and dilatancy of sands. Geotechnique, 36(1), 65–78.

    Article  Google Scholar 

  • Booker, J.R. and Small, J.C. (1975). An investigation of the stability of numerical solutions of Biot’s equations of consolidation. International Journal of Solids and Structures, 11,907–917.

    Article  Google Scholar 

  • Boulanger, R.W. and Yu, H.S. (1997). Theoretical aspects of compaction grouting in sands. Civil Engineering Research Report No. 149.07.97, The University of Newcastle, NSW 2308, Australia.

    Google Scholar 

  • Carter, J.P. (1978). CAMFE: A computer program for the analysis of a cylindrical cavity expansion in soil. Report CUED/C — Soils TR52, Department of Engineering, University of Cambridge.

    Google Scholar 

  • Carter, J.P and Yeung, S.K. (1985). Analysis of cylindrical cavity expansion in strain weakening material. Computers and Geotechnics, 1, 161–180.

    Article  Google Scholar 

  • Carter, J.P, Randolph, M.F. and Wroth, C.P. (1979). Stress and pore pressure changes in clay during and after the expansion of a cylindrical cavity. International Journal for Numerical and Analytical Methods in Geomechanics, 3, 305–322.

    Article  Google Scholar 

  • Collins, I.F. (1990). On the mechanics of state parameter models for sands. Proceedings of the 7th International Conference on Computer Methods and Advances in Geomechanics, Cairns, Australia, 1, 593–598.

    Google Scholar 

  • Collins, LE, Pender, M.J. and Wan, Y. (1992). Cavity expansion in sands under drained loading conditions. International Journal for Numerical and Analytical Methods in Geomechanics, 16(1), 3–23.

    Article  Google Scholar 

  • Koiter, W.T. (1960). General theorems for elastic-plastic solids. In: Progress in Solid Mechanics (editors: I.N. Sneddon and R. Hill), 165–221.

    Google Scholar 

  • Matsuoka, H. (1976). On significance of the spatial mobilized plane. Soils and Foundations, 16(1), 91–100.

    Article  Google Scholar 

  • Nayak, G.C. and Zienkiewicz, O.C. (1972). Elasto-plastic stress analysis: a generalization for various constitutive relations including strain softening. International Journal for Numerical Methods in Engineering, 5, 113–135.

    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 

  • Reed, M.B. (1986). Stresses and displacement around a cylindrical cavity in soft rock. IMA Journal of Applied Mathematics, 36, 223–245.

    Article  Google Scholar 

  • Roscoe, K.H. and Burland, J.B. (1968). On the generalised behaviour of wet clay. In: Engineering Plasticity (editors: J. Heyman and F.A. Leckie), Cambridge University Press, 535–609.

    Google Scholar 

  • Rowe, P. W. (1962). The stress-dilatancy relation for static equilibrium of an assembly of particles in contact. Proceedings of Royal Society, 267, 500–527.

    Article  Google Scholar 

  • Shuttle, D. and Jefferies, M. (1998). Dimensionless and unbiased CPT interpretation in sand. International Journal for Numerical and Analytical Methods in Geomechanics, 22,351–391.

    Article  Google Scholar 

  • Sloan, S.W. and Booker, J.R. (1984). Removal of singularities in Tresca and Mohr-Cou-lomb yield functions. Communications in Applied Numerical Methods, 2, 173–179.

    Article  Google Scholar 

  • Yeung, S.K. and Carter, J.P (1989). An assessment of the bearing capacity of calcareous and silica sands. International Journal for Numerical and Analytical Methods in Geomechanics, 13, 19–36.

    Article  Google Scholar 

  • Yu, H.S. (1990). Cavity Expansion Theory and Its Application to the Analysis of Pressur-emeters, DPhil Thesis, University of Oxford, England.

    Google Scholar 

  • Yu, H.S. (1994a). State parameter from self-boring pressuremeter tests in sand. Journal of G eotechnical Engineering, ASCE, 120(12), 2118–2135.

    Article  Google Scholar 

  • Yu, H.S. (1994b). A closed form solution of stiffness matrix for Tresca and Mohr-Coulomb plasticity models. Computers and Structures, 53(3), 755–757.

    Article  Google Scholar 

  • Yu, H.S. (1996). Interpretation of pressuremeter unloading tests in sands. Geotechnique, 46(1), 17–31.

    Article  Google Scholar 

  • Yu, H.S. and Houlsby, G.T. (1990). A new finite element formulation for one dimensional analysis of elastic plastic materials. Computers and Geotechnics, 9, 241–25

    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). Finite Element Solutions. In: Cavity Expansion Methods in Geomechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9596-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-9596-4_7

  • 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