Research On Propagation Characteristics Of Body Waves And Surface Waves In Unsaturated Poroelastic Medium

The problem of wave motion in poroelastic materials involves many academic subjects such as mathematics, thermodynamics and elastic mechanics. It is not only the expansion and development for the elastic medium dynamic theory, but also has extensive guidance significance for the practical engineering problems such as geotechnical engineering, petroleum engineering, geophysics, biomechanics and other fields. The previous research was based on the two-phase porous medium materials, namely the fully saturated state when the porosity of the porous materials is filled with liquid. In practice, however, most of the porous materials are in the unsaturated state, namely the gas exist in the medium pore, such as the geo-materials near the earth’s surface and the soil layer containing gas in the oil and gas field. Hence it is very important to study the wave motion problem of the unsaturated poroelastic materials. The dynamic governing equations are established basing on the triphase poroelastic medium theory in this dissertation and then the propagation problems of body waves and surface waves in these materials is analyzed deeply and systematically.In this dissertation, first of all, within the framework of generalized mixture theory, on the base of multiphase porous medium elasticity theory, according to the kinematics equations of three-phase equation, combining with mass conservation equations, momentum conservation equations, entropy inequality and relevant constitutive equations, the wave controlling equations of the unsaturated porous elastic medium in the scope of linear elastic deformation is obtained. The established three-phase wave equations can be reduced to the simplified form of Biot wave theory equations, which verifies the rationality of our equations. Then the Helmholtz decomposition method is used to solve the equations and the propagation problem of body waves in infinite space of unsaturated porous elastic medium is calculated and analyzed. By means of solving the wave equations, the characteristc equations of wave propagation are derived. The calculation results show that, three compressional waves (P1wave, P2wave, P3wave) and one shear wave (S wave) exist in the unsaturated poroelastic medium, which is consistant with the results of previous research. The influences of saturation degree and excitation frequency on the propagation characteristics such as wave velocity and attenuation coefficient are studied systematically through numerical examples. It is shown that, due to the presence of gas in the porosity, the propagation characteristics of body wave in unsaturated poroelastic medium have changed significantly.Then, on the base of linear elastic theory of unsaturated porous elastic medium, the reflection and transmission problems of body waves at various boundary conditions are respectively studied:(ⅰ) reflection problems of different body waves (P1wave and S wave) on the free surface of unsaturated porous medium,(ⅱ) reflection and transmission problems of different body waves (P1wave and S wave) on the interface between unsaturated porous medium and elastic medium,(ⅲ) reflection and transmission problems of different body waves (P1wave and S wave) on the interface between unsaturated porous medium layers with different saturation degrees. Because P1wave and S wave are the body waves with high wave velocity and low attenuation, so this dissertation mainly consider the reflection and transmission characteristics of these two body waves. In the numerical examples, the influences of frequency, incident angle and porous media saturation on the aspects such as vibration amplitude and incident wave energy distribution are discussed. The calculation results shows that, at different interface conditions, the impact of saturation change on the reflection and transmission characteristics should not be overlooked.After that, based on the wave theory of three-phase porous elastic medium, the Rayleigh wave propagation problems at the free boundary of unsaturated half-space are analyzed. According to the free boundary conditions on the half-space, the dispersion equation of Rayleigh wave is derived. It can be seen from the dispersion equation that, there are three Rayleigh wave modes, namely R1wave, R2wave and R3wave, with wave velocity R1wave> R2wave> R3wave. Through the numerical examples, the influences of porous media saturation on the propagation characteristics such as propagation velocity and attenuation coefficient are discussed. The calculation results show that the influences of frequency and saturation degree on the propagation characteristics of the different modes of Rayleigh waves are obvious.Finally, based on the unsaturated porous elastic medium wave theory and the boundary condition of the plane interface, this dissertation use the analytical method to establish and solve the Love wave dispersion characteristic equation near the boundary of unsaturated porous media. And two different cases are discussed:(1) unsaturated porous media half space is covered with a layer of elastic medium;(2) the elastic medium half-space covered with a layer of unsaturated porous media. The numerical analysis is carried out through an iterative process of dispersion equation and the influences of saturation change on the propagation velocity and attenuation coefficient are calculated and discussed. At the same time, this dissertation also has discussed the impact of media saturation degree on the cutoff frequency of high mode Love waves.In this dissertation, through a series of corresponding numerical simulation calculations, some general laws and conclusions of body waves and surface waves propagating in the unsaturated porous materials are obtained. On a theoretical level, these laws and the conclusions show that the impact of the saturation change should attract more attention in the practical engineering application fields such as soil dynamics and earthquake engineering.