Dynamic behaviour of unsaturated porous media: governing equations using the Theory of Mixtures with Interfaces (TMI)

Abstract

Theory of Mixtures with Interfaces (TMI) is used to develop field equations governing the behaviour of unsaturated porous media under dynamic loading conditions. Interfaces existing between bulk phases in unsaturated porous media are explicitly considered in the TMI. Volume fractions and area densities are introduced as independent constitutive variables. A new definition for the total stress that explicitly includes interfacial effects is deduced. Thermodynamic restrictions are used to derive the constitutive relationships. It is found that there exists a well-defined potential (i.e. Gibbs' thermodynamic potential) to drive the flow of the fluids. Effective stress for unsaturated soils is theoretically shown to dependent not only on the degree of saturation but also on the stress path and soil type. Theoretical basis for the use of two stress state variables, net stress and suction, instead of a single effective stress is provided. The soil–water characteristic curve is shown to be none other than the linear momentum balance equation of all the interfaces. Realistic functional forms are suggested to take into account the variation of suction when the solid skeleton undergoes deformation. The final set of governing equations presented are easily implementable into finite element methods and can be used to analyse problems such as the earthquake loading of compacted soil embankments. Copyright © 1999 John Wiley & Sons, Ltd.