Dilatancy in general Cambridge-type models

Cambridge-type models for soil (Cam-clay, Modified Cam-clay and NorSand) are idealised soil models based on a few simple postulates. This gives the models predictive power, and they offer interesting insight into soil behaviour. But the symmetry of the triaxial conditions for which the models were derived leaves an additional degree of freedom when generalising to arbitrary 3-D stress and strain states. The additional freedom creates unresolved inconsistencies in the plastic strain rates—usually dilatancy from the plastic potential not matching that implied by the work dissipation postulate (flow rule) under general 3-D stress states. It is shown that Cambridge-type models may be consistently generalised for arbitrary strain paths by adopting work conjugate invariants and by requiring primacy of the work dissipation postulate. The unresolved freedom for the strain rates is handled by interpolation between the limit conditions (triaxial compression and extension) that are fully defined because of symmetry. The approach is illustrated in the context of NorSand, using calibration under triaxial compression for published tests on Brasted sand to predict behaviour in the practically important case of plane strain. Excellent predictions are obtained over a range of sand densities from loose to dense.