Is the degree of saturation a good candidate for Bishop's χ parameter?

In unsaturated soil mechanics, the quest for an effective stress playing the same role as Terzaghi's effective stress does for saturated soils has introduced a long standing debate, dating back to the 1960s. Several contributions have been proposed since the early work of Bishop. It is well recognized to date that a single constitutive stress is not sufficient by itself to catch the main features of the behaviour of unsaturated soils and it is often combined with matric suction. In this paper, focus is given to a largely used formulation for such a constitutive stress, based on the use of an averaged pore pressure. In particular, this paper discusses on thermodynamics bases the validity of the choice of the factor χ weighting the fluid pressures contribution to the constitutive stress. This factor is usually assumed to be equal to the degree of saturation of water. In this work it is shown that the choice of this natural candidate implies restrictive assumptions on the plastic flow rule. As shown from experimental data obtained from a literature review, this choice may not be pertinent for certain classes of materials, particularly high plasticity clays.