  In general, the evolution of soil submitted to simple stress-strain paths is
characterised using the 3d phase space (v,p',q) i.e. (specific volume, mean
intergranular pressure, deviatoric stress q. When uniaxial compressions is
performed at constant lateral pressure p' or at constant mean pressure p', one
finds that all trajectories end up at a line of attracting point called the
critical-state line via the surface of Roscoe or of Hvorslev depending if the
initial volume is the loosest possible one (at a given p') or densest.
Trajectories of weakly dense samples are not often reported in this phase
space. We find here that they shall present some sigmoid shape as it can be
found from soil mechanics argument. This seems to indicate that Roscoe's
surface shall exhibit a singularity at the critical point.
