A new Hvorslev surface for critical state type unsaturated and saturated constitutive models

Constitutive models for unsaturated soils are most commonly based on conventional critical state type models for saturated soils. The ellipse of the modified Cam-clay model is usually adopted for the formulation of the yield and the plastic potential surfaces in the mean stress – deviatoric stress plane. Despite the wide use of this ellipse it has long been shown that the peak deviatoric stress observed for highly overconsolidated states may be largely overestimated. For fully saturated conditions, a planar surface, termed the Hvorslev surface, has been employed in the literature in order to overcome this shortcoming on the dry side of the critical state. In addition, by employing a no-tension cut-off, stress states are restricted within the compressive region. In unsaturated conditions and due to the effect of suction the soil may be subjected to tensile total stresses which should not, however, exceed a model dependent limit. Nonetheless, adopting a planar surface and in the absence of any provision, illegal tensile stresses may be obtainable. For this reason, a new expression for the Hvorslev surface, which restricts the stress state within acceptable boundaries, is proposed, based on a small number of model parameters. The new surface is curved rather than planar and can also be used in combination with critical state type constitutive models developed for saturated conditions. The new surface is calibrated based on fully saturated undrained triaxial compression and extension tests and on unsaturated drained triaxial tests. The superiority of the new surface in comparison with commonly adopted shapes for the yield and the plastic potential functions – such as the ellipse and the bullet shape of the modified and the original Cam clay models – is demonstrated through numerical analyses of the unsaturated drained triaxial laboratory tests.