Switch between fast and slow Biot compression waves induced by “second gradient microstructure” at material discontinuity surfaces in porous media

In this paper we address the problem of reflection and transmission of compression waves at planar solid-material discontinuity interfaces in second gradient porous media. We consider two types of constraints to model particular connections between two semi-infinite second gradient porous media; we call these constraints “generalized permeable clamp” and “generalized permeable hinge”. We prove that, when the two media are completely identical on the two sides of the discontinuity surface, the modalities of repartition of the energy initially carried by the incident wave among the reflected and transmitted ones can be highly influenced by the value of the second gradient parameter only when considering “generalized permeable hinges” and for sufficiently high frequencies. On the other hand, when the considered porous media have different mechanical properties on the two sides, e.g. non vanishing jumps of porosity or Young modulus, significant transfers of energy from fast to slow waves (or from slow to fast) can be observed for both types of considered constraints. Indeed, for sufficiently high frequencies, these switching phenomena can be seen to be triggered by some critical values of the second gradient parameter. The described switching phenomena are all interpreted to be directly related to the presence of an underlying micro-structure in the solid matrices of the considered porous media.