Pore-water pressure as the stress reference in the stress state variables for unsaturated soils, a theoretical revisit

Abstract

Stress state variables refer to the state of stresses that control shear strength and volume change of unsaturated soils. When the pore-water pressure, u_w, is taken as the stress reference, the stress state variables are expressed as (s - u_w), (u_a - u_w), and u_w for soils with compressible soil solids, and as (s - u_w) and (u_a - u_w) for soils with incompressible soil solids. The existing theoretical derivation was based on the equilibrium equation of water, air, and contractile skin phases. However, several steps in the existing derivation are not clearly presented and are challenging to follow. These steps are in the initial stage of the equilibrium derivation and in the elimination of the third variable, u_w, for incompressible soil solids. This paper presents revisit of the theoretical derivation to obtain the stress state variables. This revisit considers stress times area in place of force instead of stress times porosity in place of force as in the existing derivation. The proposed approach provides a clearer and more transparent procedure for eliminating u_w from the governing equations when the solid particles are assumed to be incompressible. This revisit also provides sound stress state variables for unsaturated soils with both compressible and incompressible solids. Overall, the theoretical revisit in this paper offers clearer interpretation and a more comprehensible derivation. In addition, it supports the validity and correctness of the commonly adopted stress state variables used in the constitutive modelling of unsaturated soils.