ABSTRACT
Biot’s model is applicable when the elastic skeleton presents a simple porosity, and when the saturating fluid is Newtonian, weakly compressible, and flows in a laminar static or dynamic regime. The aim of this study is to give the modified descriptions when some of these assumptions are changed. We successivelly consider, the case of a viscoelastic saturating fluid, double porosity media, the acoustics of porous media saturated by air, and finally, the deviation of the Darcy’s law for non linear flows. The various models corresponding to these different hypotheses were deduced by coupling first, a physical analysis leading to a dimensionless formulation of the involved phenomena, and second, the method of homogenization of periodic media for deducing the macroscopic behaviour from the description at the microscopic scale.
