On the analytical solutions for the three-invariant Cam clay model

The analytical solutions are presented for a generalized shear strain, based on the three-invariant Cam clay model. The solutions are derived for an undrained loading by adopting the assumption of incompressibility, which is valid for any fully saturated soil. Two loading histories are considered: the so-called proportional and circular loading. They correspond to the situations where Lodeʹs angle θ is either constant or changing during loading, respectively. The maximum possible change in Lodeʹs angle for any circular loading is equal to π⧸3 due to plastic isotropy. Failure occurs within this segment only for the cases which are loaded from higher initial values of the overconsolidation ratio. The solutions presented here complete the picture of the undrained stress–strain-strength behavior for the soft clays by defining the analytical relationship between a shear strain and a stress ratio.