A reduced model to locate low contrast inclusions in poroelastic media

This paper introduces a numerical method to localize inclusions having slightly different elastic coefficients than those of a fully saturated poroelastic matrix, whose detection is often difficult. This method can be used to find weakly stiffer or softer objects in saturated soils or diseased biological tissues at early stages. To this end, we propose a reduced model from the Biot's equations by splitting the fluid pressure into two parts: one embedded into an elasticity model and the other one used as a corrector term. By applying the small amplitude homogenization method, we can successfully retrieve the position and extension of inclusions in poroelastic media employing this simplified model. Numerical results show a good agreement for the location of inclusions when the contrast is below 30% stiffer or softer than the matrix, and for a noise level up to 5% for frequencies below 50 Hz.