Modification of Biot’s theory of porous materials

Abstract

Acoustic waves in porous material are traditionally investigated by using Biot’s theory to describe the elastic wave propagation in such materials. However, experimental results obtained by models of porous media made of cohesionless particles forming loose solid matrix with fluid-filled pores, contradict the above theory at high frequencies. These results show that the acoustic wave speed as a function of frequency and particle size goes through a maximum and then decreases with frequency until a cutoff frequency is reached, whereas Biot’s theory predicts an asymptotic increase of propagation speed with frequency, without a wave cutoff frequency. The theoretical analysis and the experimental investigation are presented that modify and adapt Biot’s theory to the cohesionless porous materials. The equations describing these modifications to the theory take into account the following effects: the contact surfaces between the solid particles, their number concentration, the size of the solid particles, the depth at which they are situated, the external pressure, their random arrangement, and the propagation direction of the acoustic waves.