| Wave propagation theory and sound absorption theory in porous materials have extensive and important applications in oil exploration, oil drilling, rock and soil mechanics, earthquake engineering, materials science and acoustic fields. This paper first studies the single porous medium of Biot’s Theory and Berryman’s scientific research, then extend them to the double porosity medium in order to obtain the wave propagation equations. By using the Helmholtz resolution method, we decouple the solid matrix, matrix pore and fracture pore coupling equations. A series of scattering of elastic waves equations are obtained by using the wave function expansion method. Then with the help of transformation theory for spherical coordinates and the superposition principle, the scattering problem of double spherical inclusions can be expressed in the same coordinate system. Finally, examples of calculation and analysis of different parameters are concerned to determine what impacts they have on first order wave amplitude with variation to frequency. The results show that: different porosity, matrix permeability and inclusion radius have significant impact on P1-P3 wave and S-wave amplitude; However, the matrix porosity has little impact on P3 wave; Also the fracture porosity has little significance on P2 wave; Matrix permeability affects only P2 wave amplitude, and its value increases as the matrix permeability decreases, while the P1 wave, P3 wave and S-wave amplitude stay almost unaffected.In the double spherical inclusions model, the value of P1-P3 wave and S-wave amplitude decrease as the distance between the inclusions increases; In addition P1 wave and S-wave amplitude have significant changes while P2 wave has relatively small change. Besides, the value of P1-P3 wave and S-wave amplitude increase as the radius of the other inclusion increases. The radius has more impact on P1 and P3 wave but has rather small influence on P2 wave and S wave amplitude. |
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