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

In engineering applications involving mechanics of geomaterials, focus is generally put on the deformation of the solid skeleton so that a great interest is given to the definition of the stresses governing the skeleton deformation. The presence of one or several fluids within the porous space of these materials introduces a complexity in the choice of the stress state variables with respect to non-porous materials. (Terzaghi, 1936) stated that in the case of saturated soils (where a single fluid filling the porous space) a single stress (called effective stress) governs the deformation and strength. Roscoe and his co-workers (Roscoe et al., 1958) applied the mathematical theory of plasticity to saturated soil mechanics introducing the concept of critical state. This work resulted in the well-known Camclay model for saturated soils involving Terzaghi’s effective stress. An extension of this model to unsaturated soils has been proposed by Alonso et al. (Alonso et al., 1990) within a simple elastoplastic framework. This extension points out the need of two independent state variables to capture the experimentally observed behaviour of unsaturated soils instead of a unique stress variable (effective stress) in the case of saturated states. Later on, this model settled the bases of numerous models, addressing additional features of unsaturated soils behaviour, such as the effects of water content (Wheeler, 1996) or degree of saturation (Jommi and Di Prisco, 1994, Dangla et al., 1997, Lewis and Schrefler, 1998, Gallipoli et al., 2003, Sheng et al., 2004, Pereira et al., 2005) among others. Advances on the last point have reintroduced a strong debate dated back to the 1960s with Bishop’s proposal for an extended effective stress σ’ to unsaturated states (Bishop, 1959) who introduced an averaging parameter χ, this latter being a function of the water degree of saturation Sr: