On undrained test using Rowe's relation and Incremental Modelling: Generalisation of the notion of Characteristic State

It is recalled that stress-strain incremental modelling is a common feature of most theoretical description of the mechanical behaviour of granular material. An other commonly accepted characteristics of the mechanical behaviour of granular material is the Rowe's relation which links the dilatancy K to the ratio B of vertical-to-lateral stress during a test at constant lateral stress, i.e. B =(1+M)(1+K). Using an incremental modelling, this law shall be interpreted as a pseudo-Poisson coefficient. We combine these two features to solve the problem of an axial compression under undrained condition. We demonstrate that the sample is submitted to a bifurcation of the transcritical type when it reaches the q=Mp line. This allows extending the notion of the characteristic state introduced by Luong to other situations and to anisotropic systems. We show also that these undrained tests are quite appropriate to study the characteristic-state behaviour.