  The aim of the present study is to derive the effective quasi-static
behaviour of a composite medium, made of a poroelastic matrix containing
elastic impervious inclusions. For this purpose, the asymptotic homogenisation
method is used. On the local scale, the governing equations include Biot's
model of poroelasticity in the porous matrix and Navier equations in the
inclusions, with elastic properties of the same order of magnitude. Biot's
diphasic model of poroelasticity is obtained on the macroscopic scale, but with
effective parameters that are strongly impacted by the distribution of
inclusions, even at low volume fraction. The impact on fluid flow is strictly
geometrical, showing that the inclusions do not play the role of a porous
network.
