Mechanics of continuous porous media

Soils consist of an assemblage of particles with different sizes and shapes which form a skeleton whose voids are filled with water and air or gas. The word "soil", therefore, implies a mixture of assorted mineral grains with various fluids. When free or no drainage conditions prevail, a single phase description of soil behavior is adequate. However, in intermediate cases in which some flow can take place, there is an interaction between the skeleton strains and the water flow. The solutions of these problems require that soil behavior be analyzed by incorporating the effects of the transient flow of the pore-fluids through the voids, and, therefore, requires that a multiphase formulation be available for porous media. Such a theory was first proposed by Biot, early in 1955, for a linear elastic and a linear visco-elastic porous medium. However, it is observed experimentally that the stress-strain-strength behavior of the soil skeleton is strongly non-linear, anisotropic, elastoplastic and path-dependent. An extension of Biot's theory into the nonlinear anelastic range is, therefore, necessary in order to analyze the transient response of soil deposits. This extension has acquired considerable importance in recent years due to the increased concern with the dynamic behavior of saturated soil deposits and associated liquifaction of saturated sand deposits under seismic loading conditions. Such an extension of Biot's formulation is proposed herein.