Topology of Roscoe's- and Hvorslev's- Surfaces in the Phase Space of   Soil Mechanics
  In general, the evolution of soil submitted to simple stress-strain paths is characterized using the 3d phase space (v,p',q) i.e. (specific volume, mean intergranular pressure, deviatoric stress); one finds that all trajectories end up at a line of attracting point called the critical-state line. The surface of Roscoe (Hvorslev) is defined as the surface made of the last part of the set of trajectories ending to a given critical point and coming from all states of normally consolidated soils (from all states of over consolidated soils). It is demonstrated that these two sets are part of the same surface, which is confirmed by experimental data. 
P. Evesque