Coupling equations for variably saturated geomaterials. A mathematical model for non-isothermal multiphase porous materials: fundamentals and formulation

A mathematical model for a fully saturated and partially saturated non-isothermal porous medium in dynamics is presented. The porous material is treated as a multi phase continuum with the pores of the solid skeleton filled by one or more fluids, e.g. liquid water and gas phase, which may be either water vapour alone or a mixture of dry air and water vapour. The governing equations at macroscopic level are de rived in a spatial setting using averaging theories from balance equations developed at microscopic level. Finite kinematics is included in the model. The solid skeleton of the medium can undergo large elastic or inelastic deformations described in the framework of hyperelastoplasticity.