Constitutive Laws for Normally Consolidated Clay

The following expression of the yield locus of the normally consolidated clay is derived from the energy equation by applying the normality condition:where p and q are the mean normal effective stress and the deviatoric stress respectively; p0 is the equivalent isotropic consolidation pressure of the given stress state （p,q）; α, β and γ are parameters which determine the geometry of the yield locus. It is shown that this expression is identical with that previously （1964） obtained by the author from the data of undrained stress path in the conventional triaxial compression tests. Then by means of the concept of the plastic potential and the associated flow rule the general formula of the elasto-plastic stress-strain relationship for the normally consolidated clay is obtained as follows; where Md = D/p; Mk = 1/μ; Mg = p/（DG）; and D, μ and G represent the coefficient of dilatancy, coefficient of pore pressure and shear modulus respectively. Furthermore the simplified forms of the above formula for some special cases are also derived. The proposed model has been used to predict the behaviour of the samples in the conventional drained and undrained triaxial compression tests, and the comparison of these results with a few available experimental data indicates that the prediction by the proposed model agrees with the tests better than the modified Cam clay model. In fact, the latter is just a special case of the model proposed by the author.