Use of porosity in models of consolidation

Porosity is a fundamental variable used in the small strain theory of consolidation to measure the volume of the pore space in the volume of soil. It is defined as a ratio of the two variables, as opposed to volumetric strain, which measures the change in volume of soil only. Porosity increment represents both changes in the pore space and in the volume of the soil element. Such changes originate by stress changes and/or by environmental changes (temperature, moisture, or chemistry). Three different definitions of porosity are commonly adopted in the modeling of porous deformable materials, originated by the theories of Terzaghi, Biot, and Hassanizadeh. When changes in the pore volume and the volume of the material element are of the same order, the differences in definition of porosities may induce significant differences in values of their increments. Lagrangian, material, and spatial porosity increments are defined and compared. The continuity equation used in Terzaghi's model of consolidation is derived from multiphase mixture theory to show consistent and inconsistent uses of the porosity increments.