The Research On Scattering By A Inclusion In Double-Porosity Medium

For the past few years, the research on the theory of elastic wave in double-porosity mediumare paid more and more attention by scholars, especially the problem that scattering of elastic waveby inclusion in double-porosity medium is always a challenging subject in scientific community, ithas a far-reaching significance in both physics, seismology and mechanics. Many situation inengineering have to take the correlations of scattering effect and mechanics properties of complexporous medium into account, for example, nondestructive testing of composite material, mineralprospecting and oil exploration, technique of radar and sonar.Although there are many scholars did a fair amount of effective work on the problem thatscattering of elastic wave by inclusion in homogeneously elastic medium and single-porositymedium so far, there are few studies about double-porosity medium, especially the scattering ofelastic wave by inclusion in double-porosity medium. In this paper, base on the extended Biot'stheory of poroelasticity and double-porosity model which founded by Berryman and Wang, byusing the wave expansion method, the scattering of longitudinal wave by a spherical ideal fluidinclusion in double-porosity medium is investigated. An explicit analytical solutions for theharmonic amplitude, displacement field and stress field of the problem were obtained. Then thepaper investigated the spherical harmonic amplitude of P1~P3wave, S wave in plane problem andSH wave, SV wave in three-dimension problem in the scattered field by numerical analysis, andsummarized the rules. The results of the calculation show that matrix porosity, fracture porosity,radius of inclusion and matrix permeability have obvious influence on spherical harmonic amplitudeof scattered wavefield. And the influence of matrix porosity, fracture porosity, radius of inclusionand matrix permeability would become more obviously while the frequency increase. But the matrixporosity has no influence on the spherical harmonics amplitude of P3wave scattered field, and fracture porosity has little influence on the spherical harmonic amplitude of P2wave scattered fieldboth in the plane problem and the three-dimension problem. Matrix permeability only has influenceon spherical harmonic amplitude of P2wave scattered field, in other words, matrix permeability hasno influence on the spherical harmonics amplitude of P1waves scattered field, P3wave scatteredfield, S wave scattered field in plane problem and SH wave scattered field, SV wave scattered fieldin three-dimension problem. The compressional waves in the plane scattering problem have thesame rules as the corresponding compressional waves in the three-dimension scattering problem,under different matrix porosity, fracture porosity, radius of inclusion or matrix permeability. The Swave in the plane scattering problem and the SH wave in the three-dimension scattering problemhave the similar relationship. As the change of matrix porosity, fracture porosity, radius of inclusionor matrix permeability under the same frequency, the compressional waves in the plane scatteringproblem have the same change scale with the corresponding compressional waves in thethree-dimension scattering problem. The S wave in the plane scattering problem and the SH wave inthe three-dimension scattering problem also have the similar relationship.