DOI QR코드

DOI QR Code

Analytical solution for undrained plane strain expansion of a cylindrical cavity in modified cam clay

  • Silvestri, Vincenzo (Department of Civil, Geological, and Mining Engineering, Ecole Polytechnique) ;
  • Abou-Samra, Ghassan (Department of Civil, Geological, and Mining Engineering, Ecole Polytechnique)
  • 투고 : 2011.03.23
  • 심사 : 2011.12.28
  • 발행 : 2012.03.25

초록

This paper presents the results of analytical and numerical analyses of the effects of performing a pressuremeter test or driving a pile in clay. The geometry of the problem has been simplified by the assumptions of plane strain and axial symmetry. Pressuremeter testing or installation of driven piles has been modelled as an undrained expansion of a cylindrical cavity. Stresses, pore water pressures, and deformations are found by assuming that the clay behaves like normally consolidated modified Cam clay. Closed-form solutions are obtained which allow the determination of the principal effective stresses and the strains around the cavity. The analysis which indicates that the intermediate principal stress at critical state is not equal to the mean of the other two principal stresses, except when the clay is initially isotropically consolidated, also permits finding the limit expansion and excess pore water pressures by means of the Almansi finite strain approach. Results are compared with published data which were determined using finite element and finite difference methods.

키워드

참고문헌

  1. Baguelin, F., Jezequel, J.F., Lemee, E. and LeMehaute, A. (1972), "Expansion of cylindrical probes in cohesive soils", J. Soil Mech. Found. Div. - ASCE, 98(11), 1129-1142.
  2. Baguelin, F., Jezequel, J.F. and Shields, D.H. (1978), The pressuremeter and foundation engineering, Trans Tech Publications, Clausthall, Germany.
  3. 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", Int. J. Numer. Anal. Method. Geomech., 3(4), 305-322. https://doi.org/10.1002/nag.1610030402
  4. De Sousa Coutinho, A.G.F. (1990), "Radial expansion of cylindrical cavities in sandy soils: application to pressuremeter tests", Can. Geotech. J., 27(6), 737-748. https://doi.org/10.1139/t90-087
  5. Gibson, R.E. and Anderson, W.F. (1961), "In-situ measurement of soil properties with the pressuremeter", Civil Eng. Public Works Rev., 56(658), 615-618.
  6. Hill, R. (1950), The mathematical theory of plasticity, Oxford University Press, London, England.
  7. Hill, R., Lee, E.H. and Tupper, S.J. (1947), "The theory of combined plastic and elastic deformation with particular reference to a thick tube under internal pressure", Proceedings of the Royal Society of London, Series A, 191(1026), 278-303. https://doi.org/10.1098/rspa.1947.0116
  8. Itasca. (1995), FLAC Version 3.3. Itasca Consulting Group, Inc., Minneapolis.
  9. Ladanyi, B. (1972), "In-situ determination of undrained stress-strain behaviour of sensitive clays with the pressuremeter", Can. Geotech. J., 9(3), 313-319. https://doi.org/10.1139/t72-034
  10. Mendelson, A. (1968), Plasticity: theory and application, MacMillan, New York.
  11. Nadai, A. (1950), Theory of flow and fracture of solids, Vol.1. McGraw-Hill, New York.
  12. Palmer, A.C. (1972), "Undrained plane-strain expansion of a cylindrical cavity in clay: a simple interpretation of the pressuremeter test", Geotechnique, 22(3), 451-457. https://doi.org/10.1680/geot.1972.22.3.451
  13. Peric, D. and Ayari, M.A. (2002), "On the analytical solution for the three-dimensional invariant Cam clay model", Int. J. Plasticity, 18, 1061-1082. https://doi.org/10.1016/S0749-6419(01)00028-6
  14. Randolph, M.F., Carter, J.P. and Wroth, C.P. (1979), "Driven piles in clay-the effects of installation and subsequent consolidation", Geotechnique, 24(4), 361-393.
  15. Silvestri, V. and Abou-Samra, G. (2011), "Application of the exact constitutive relationship of modified Cam clay to the undrained expansion of a spherical cavity", Int. J. Numer. Anal. Method. Geomech., 35(1), 53-66. https://doi.org/10.1002/nag.892
  16. Silvestri, V. and Abou-Samra, G. (2009), "Analytical solution of stress-strain relationship of modified Cam clay in undrained shear", Geomechanics & Engineering, 1(4), 263-274. https://doi.org/10.12989/gae.2009.1.4.263
  17. Wood, D.M. (2007), Soil behaviour and critical state soil mechanics, Cambridge University Press, Cambridge.
  18. Yu, H.S. (2000), Cavity expansion methods in geomechanics, Kluwer Academic Publishers, Dordrecht, The Netherlands.

피인용 문헌

  1. A rigorous semi-analytical solution for undrained cylindrical cavity expansion in critical state soils vol.40, pp.15, 2016, https://doi.org/10.1002/nag.2529
  2. Analysis of Undrained Cylindrical Cavity Expansion Considering Three-Dimensional Strength of Soils vol.16, pp.5, 2016, https://doi.org/10.1061/(ASCE)GM.1943-5622.0000650
  3. Analysis and modeling of the percussion coring of an innovative hydrostatic sediment corer vol.134, 2017, https://doi.org/10.1016/j.oceaneng.2017.02.005
  4. Stress state around cylindrical cavities in transversally isotropic rock mass vol.6, pp.3, 2014, https://doi.org/10.12989/gae.2014.6.3.213
  5. Similarity solution for cavity expansion in thermoplastic soil vol.42, pp.2, 2018, https://doi.org/10.1002/nag.2724
  6. Application of Cylindrical Cavity Expansion in MCC Model to a Sensitive Clay under Ko Consolidation vol.30, pp.8, 2018, https://doi.org/10.1061/(ASCE)MT.1943-5533.0002328
  7. A displacement solution for circular openings in an elastic-brittle-plastic rock vol.13, pp.3, 2012, https://doi.org/10.12989/gae.2017.13.3.489
  8. A numerical stepwise approach for cavity expansion problem in strain-softening rock or soil mass vol.18, pp.3, 2012, https://doi.org/10.12989/gae.2019.18.3.225
  9. Elasto-plastic solution for cavity expansion problem in anisotropic and drained soil mass vol.19, pp.6, 2019, https://doi.org/10.12989/gae.2019.19.6.513
  10. A novel approach for predicting lateral displacement caused by pile installation vol.20, pp.2, 2020, https://doi.org/10.12989/gae.2020.20.2.147
  11. Numerical simulation of set-up around shaft of XCC pile in clay vol.21, pp.5, 2012, https://doi.org/10.12989/gae.2020.21.5.489
  12. Installation effects of the post-grouted micropile in marine soft clay vol.15, pp.12, 2012, https://doi.org/10.1007/s11440-020-00993-x
  13. Research on multi-frequency ultrasonic scanning detecting technology of cavity in the test borehole vol.80, pp.2, 2012, https://doi.org/10.1007/s10064-020-01979-5
  14. Prediction of Unloading Failure Strain and Undrained Shear Strength of Saturated Clays by Limit Pressure from Prebored Pressuremeter vol.44, pp.5, 2012, https://doi.org/10.1520/gtj20200222
  15. Numerical modelling of the long-term effects of XCC piling in fine-grained soil vol.26, pp.1, 2012, https://doi.org/10.12989/gae.2021.26.1.027
  16. Anisotropic borehole response from pressuremeter testing in deep clay shale formations vol.58, pp.8, 2012, https://doi.org/10.1139/cgj-2019-0801
  17. A similarity solution for spherical cavity drained expansion in overconsolidated soils considering large deformation vol.26, pp.5, 2021, https://doi.org/10.12989/gae.2021.26.5.427