Mathematical models for soil consolidation problems: a state of the art report

The mathematical modeling of the consolidation theory is outlined moving from the fundamentals of the mechanics of porous media. Starting from averaging approaches or from the postulates of the theory of mixtures, we introduce the volume fraction concept, the balance equations for the components of the mixture (written in Eulerian and Lagrangean frames of reference) and the concept of effective stress. Initial boundary value problems are considered for typical geotechnical applications, and in this context Biot’s theory is illustrated. A final discussion concerns the mathematical priciples that are to be accomplished when formulating constitutive relationships.