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Geomechanics and Engineering
  Volume 4, Number 1, March 2012, pages 19-37

Analytical solution for undrained plane strain expansion of a cylindrical cavity in modified cam clay
Vincenzo Silvestri and Ghassan Abou-Samra

    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.
Key Words
    undrained cylindrical expansion; plane strain; modified Cam clay; stress-strain curves; analytical and numerical analyses; comparisons.
Department of Civil, Geological, and Mining Engineering, Ecole Polytechnique, P. B. 6079,
Station Centre-Ville, Montreal, Quebec, Canada H3C 3A7

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