Browse > Article
http://dx.doi.org/10.12989/gae.2012.4.1.019

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)
Publication Information
Geomechanics and Engineering / v.4, no.1, 2012 , pp. 19-37 More about this Journal
Abstract
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.
Keywords
undrained cylindrical expansion; plane strain; modified Cam clay; stress-strain curves; analytical and numerical analyses; comparisons;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Itasca. (1995), FLAC Version 3.3. Itasca Consulting Group, Inc., Minneapolis.
2 Ladanyi, B. (1972), "In-situ determination of undrained stress-strain behaviour of sensitive clays with the pressuremeter", Can. Geotech. J., 9(3), 313-319.   DOI
3 Mendelson, A. (1968), Plasticity: theory and application, MacMillan, New York.
4 Nadai, A. (1950), Theory of flow and fracture of solids, Vol.1. McGraw-Hill, New York.
5 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.   DOI
6 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.   DOI   ScienceOn
7 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.
8 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.   DOI   ScienceOn
9 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.   DOI
10 Wood, D.M. (2007), Soil behaviour and critical state soil mechanics, Cambridge University Press, Cambridge.
11 Yu, H.S. (2000), Cavity expansion methods in geomechanics, Kluwer Academic Publishers, Dordrecht, The Netherlands.
12 Hill, R. (1950), The mathematical theory of plasticity, Oxford University Press, London, England.
13 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.   DOI
14 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.
15 Baguelin, F., Jezequel, J.F. and Shields, D.H. (1978), The pressuremeter and foundation engineering, Trans Tech Publications, Clausthall, Germany.
16 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.   DOI   ScienceOn
17 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.   DOI
18 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.