Research On Propagation Characteristics Of Elastic Waves In Biot-type Three-phase Medium

Geotechnical media,as the most widely existing engineering materials on the earth,are typical multi-phase porous media.The problem of wave motion in porous media involves many subjected such as mathematics and mechanics,and has important academic and applied value in many fields such as civil engineering,environmental engineering,energy engineering,exploration engineering,seismic engineering and geophysics.Since the establishment of Biot theory,the study of wave propagation in two-phase porous media has become more and more mature after decades of efforts by scholars at home and abroad,and the study of wave propagation in unsaturated three-phase porous media and dual-porous media has been gradually carried out.In fact,some porous media,such as permafrost,pore-space gas hydrate-bearing sediments and argillaceous sandstones,may have pore-solid in addition to pore-water and pore-gas in their pore space.Pore-solid and porous skeleton often have different mechanical behaviors depending on the content and distribution patterns of pore-solid.Therefore,it is more reasonable to regard them as two different phases.In this paper,three-phase porous media assumed to be a continuum consisting of sediment grains with connected pores occupied by the mixture of a pore-water and a pore-solid are studied.Based on the previous work,introducing a contact parameter to characterize the interaction between the porous skeleton and the pore-solid,we modify the Biot-type three-phase theory by the Hamiltonian principle and the Lagrangian equation.The Helmholtz decomposition method is used to solve the equations and the propagation characteristics of body waves in Biot-type three-phase media are calculated and analyzed.The types,phase velocity and attenuation of body waves in porous skeleton single-phase system,porous skeleton/pore-water biphase system,and porous skeleton/pore-water/pore-solid three-phase system are compared,and the effects of porous skeleton properties such as porosity and consolidation coefficient,pore-solid properties such as saturation and contact parameters on the phase velocity and attenuation of body waves are analyzed.Then,based on the Biot-type three-phase theory,the dynamic response of gas hydrate-bearing sediments at the incident of P1 and S1 waves is studied.The effects of incident angle,saturation and contact parameters are analyzed,as well as the environmental factors such as incident wave frequency and permeability conditions.The difference and relationship between the dynamic response based on three-phase porous media and that based on two-phase media are compared when pore-solid are in suspension in pore-water or the pore-solid and porous skeleton are essentially.Then,the reflection and transmission models at the interface of between ideal fluid and Biot three-phase porous media are established when the incident wave is P wave in the ideal fluid or P1(S1)-wave in the Biot three-phase media,respectively.The directions of propagation vectors and attenuation vectors of reflected and transmitted waves are also discussed.The effects of incident angle,saturation,contact parameters,frequency and permeability conditions on the amplitude rate,phase transition,energy flow rate and displacement at the interface are analyzed by numerical examples.Based on the Biot-type three-phase theory,ideal fluid theory and linearized viscous fluid theory,the pseudo-Rayleigh wave propagation of Biot-type three-phase porous media at the free permeable/impervious interface and the pseudo-Scholte wave propagation model of ideal fluid/Biot-type three-phase porous media at the permeable and impervious interface are established.The effects of frequency,permeability conditions,saturation,and contact parameters on the phase velocity,phase velocity ratio,attenuation coefficient and generalized displacement field induced by interface wave are analyzed by numerical calculation.Finally,the pseudo-Scholte wave propagation model of viscous fluid/Biot three-phase porous media at the permeable and impermeable interface is established.The rationality of treating water as an ideal fluid is proved and when the viscous fluid needs to be considered are studied.