An Enhanced Solution for the Expansion of Cylindrical Cavities in Modified Cam Clay

A solution was recently obtained for the expansion of cylindrical cavities in normally consolidated Modified Cam Clay under plane strain and undrained conditions. Constitutive relationships which combined the elastic and plastic responses of the clay were derived by assuming that the shear modulus, G′, and the hardening parameter, p′_c, which controls the size of the yield locus, remained constant throughout the expansion. The latter assumption resulted in some unexpected findings. It was found, for example, that the ratio between the axial stress σ_{z f} and the sum of the remaining radial and tangential stresses, σ_{r f} and σ_θf at critical state, closely approached but never attained the theoretical value of 0.5, except for the particular case of K_o = 1, where K_o is the coefficient of lateral earth pressure. The present paper removes the restrictive assumption on the hardening parameter, p′_c, which now varies during the shearing process. New effective stress relationships are obtained and the solution is applied for illustration purposes to both normally consolidated and overconsolidated Boston Blue Clay, for which the overconsolidation ratio (OCR) varies between 1 and 32. Results are compared to a well - known benchmark solution obtained by means of finite element analyses.