| The determination of the equivalent properties of heterogeneous porous rocks arises in a range of geoscience problems,such as oil exploration,seismology eneineering,CO2 storage and groundwater flow analysis.A common method of detecting crustal rocks is based on the use of elastic wave.Thus,it is of particular interest to develop equivalentdynamic models for heterogeneous rocks.Due to the heterogeneity,the propagation of elastic wave in fluid-filled rocks will induce local unsteady flow.Within the seismic band of frequencies(1-1000 Hz)and the sonic logging band of frequencies(1-20 kHz)such wave-induced local fluid flow(WILFF)is believed to be the major mechanism in causing the body-wave velocity dispersion and measured level of energy loss(inverse quality factor approximately lies within 0.01-0.1).In this thesis,the influences of two typical WILFFs,the microscopic-scale squirt flow and mesoscopic-scale diffusion flow on the elastic body wave dispersion are studied.Equivalent-dynamic models of squirt-flow type and diffusion flow type are developed.An inclusion-based model of squirt flow is developed to quantify the the velocity dispersion and attenuation of elastic body waves.It is shown that the grain-scale fluid transport due to the squirt flow mechanism can be interpreted by the concept of eigenstrain.Based on Hill's average principle an expression of the effective modulus tensor of a cracked porous rock is derived.Meanwhile,linear constitutive relation is proposed to connect macroscopic properties to microscopic heterogeneity of pore microstructure.Eshelby's single inclusion theory is extended to deseribe the pore deformation while considering the fluid transportation.Mori-Tanaka scheme is extended to quantify the squirt-flow dispersion with aid of the law of mass conservation of pore fluid.The inclusion-based model is compatible with Gassmann's equations at lowfrequency limit.The model can be used even if the stiff porosity is zero because it is not assumed the stiff porosity is greater than the soft porosity.The model is able to quantify the transverse wave dispersion.Extension of the present model to a unified model of macroscopic seepage flow and squirt-flow is easy.Based on inverted data of the crack aspect ratio distribution we calculate the P wave attenuation.It is shown that the mechanism of squirt-flow contributes to significant attenuation at seismic frequencies.Prior research of mesoscopic-scale diffusion flow mainly focuses on understanding the effective bulk modulus dispersion or deriving a effective longitudinal wavenumber of heterogeneous rocks.In contrast,the transverse wave dispersion problem has been rarely studied.In this paper,the mechanical responses of a heterogeneous poroelastic medium containing spherical or cylindrical inhomogeneities are studied when shear stress are applied.Based on a three-phase structure which is made up of an inner inhomogeneity,an outer equivalent medium and an intermediate matrix,the effective shear modulus of such unit cell is derived.The expression is valid for low frequencies at which the inhomogeneity diameter is smaller than the transverse wavelength.It is found that the inhomogeneity behaves like a quadrupole of fluid mass source so that the net fluid content change within the inhomogeneity is zero.But as long as the local fluid exchange occurs,the shear modulus will disperse causing transverse attenuation.Stiff inclusions imbedded in a relatively soft matrix can cause significant attenuation at seismic frequency bands,but soft inclusions imbedded in a relatively stiff matrix cause very weak attenuation.The mixed heterogeneity in both the solid frame and pore fluid also has important influences on the dispersion.In addition,the impact of spatial elastic properties and permeability fluctuations on the dynaic behavior of porous media is studied.Based on the first order statistical smoothing method,we develop a visco-equivalent elasticity model and a dynamicequivalent permeability model for randomly heterogeneous porous media.In particular,we analyze the influences of the heterogeneous parameters,characteristic length and frequency on the dispersion of dynamic permeability.The results suggest that there exist two hydraulic diffusion modes in heterogeneous porous media.Both modes exhabit positive permeability dispersion.At low frequencies,the high-permeability mode dominates the fluid transportation while the low-permeability mode is negligible.But at high frequencies,both modes are equally important.It is also show that extimation of flow permeability from seismic attenuation is not accurate if the slow wavelength is smaller than the characteristic length of the heterogeneity.Predicting the near-tip mechanical responses of a crack during elastic wave propagation is important for understanding aftershocks.When an earthquake occurs,longitudinal wave travels the fastest and arrive at zones of interests first,giving arise to the change of stresses and pore pressure.In this study,the scattering of elastic wave by a fluid-saturated permeable circlar with oblique incidence of the plane longitudinal wave in an infinite poroelastic medium is studied.The problem is formulated in cylindrical coordinates and solved by Hankel integral transform method.The total scattered field is divided into a symmetric part and an anisymmetric part with respect to the plane of the crack.The solution method is based on expansion of stresses and displacements on the crack surface in terms of trigonometric functions and Legendre functions.With the aid of orthogonality relation and boundary conditions,the expansion coefficients of scattered field are related to those of incident field through an infinite matrix.The stress intensity factors,the scattering cross section and scattered far fields are explicitly expressed in terms of expansion coefficients.Numerical examples show that the frequency-dependent behavior of the mode I stress intensity factor of a fluid-saturated permeable fracture is quite different from that of an impermeable traction-free fracture.For the impermeable fracture,the stress intensity factor first goes up,and then goes down.The maximum value of the stress intensity factor occurs when the wavelength approximates to the fracture diameter.In contrast,the mode I stress intensity factor of a permeable fracture is significantly affected by the phenonmenon of the wave-induced fluid flow.The stress intensity factor monotonically decreases with increasing frequency,declining the fastest when the slow wavelength approximates to the fracture diameter.As frequency increases the fluid inside the fracture support more stress,lowering stress singularity of the fracture tip.It is also shown that the fracture size affect Therefore this poroelastic effect should not be neglected.It is also shown that the low-frequency asymptotic behavior of the scattering cross section is different from thehigh-freuqnecy situation.The transition frequency occurs when the slow wavelength and the fracture diameter are of the same order. |
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