Potentials for the modified Cam-Clay model

Energy and dissipation pseudo-potentials are employed to derive constitutive relationships, in the context of thermodynamic concepts, for the widely used Modified Cam-Clay (MCC) model for soil mechanics. A variational formulation of the MCC evolution equations is proposed in this paper. Since plastic collapse of MCC soils cannot be embedded in the classical limit analysis theory, finding the critical amplification of the load that produces plastic collapse is formulated in the form of a system of equations and inequalities. Then, a mixed minimization principle is proposed for the plastic collapse analysis of MCC soils. This principle is obtained by the application of the variational formulation for the flow law introduced in the first part of the article.