Derivation of the work expression and discussion on the effective principle and the phase separation theorem in unsaturated soil

Abstract

Based on the balance equations for mass, linear momentum, energy in porous media theory and some hypotheses in unsaturated soil mechanics, an expression of the total deformation work W is derived, and with the help of the specific expression of the work, the effective stress conjugated with the displacement of the soil skeleton is suggested by the authors, which has the similar form as the expressions proposed by Wheeler (2003) and some other researchers according to their experience and intuition, but the effective stress presented in this paper is derived on the basis of porous media theory and its assumptions, whose premise and hypothesis are clear. It is also pointed out that due to the complexity of the physical mechanism and various influencing factors, it is impossible in unsaturated soil mechanics to determine the deformation of solid skeleton by the effective stress only, like in the saturated soil mechanics. Besides, by using the expression of the deformation work and the free energy Aα for each phase, the applicability of the Phase Separation Principle proposed by Passman (1984) in unsaturated soil is discussed, and it is considered that the principle should not strictly apply to unsaturated soil mechanics.