饱和多孔微极介质的波动方程及其势函数方程

土是由一定尺寸大小颗粒所构成的多孔介质,具有明显的颗粒特性,当土颗粒间的孔隙被流体（如水或油）充满时则成为饱和土.利用微极理论和Biot波动理论的研究成果,把饱和土中多孔固体骨架部分近似地视为微极介质,孔隙中的流体部分视为质点介质,获得饱和多孔微极介质的弹性波动方程.借鉴Greetsma理论,建立了饱和多孔微极介质弹性本构方程力学参数与相应单相介质弹性参数的相互关系,使饱和多孔微极介质弹性波动方程中的物理参数具有明确的物理意义,易于在试验中确定.运用场论理论把饱和多孔微极介质的波动方程简化为势函数方程,建立了饱和多孔微极介质中五种弹性波的弥散方程,数值分析了五种简谐体波在无限饱和多孔微极介质中的传播特性. 结果表明,P1波、P2波和剪切S1波的波速弥散曲线与经典饱和多孔介质基本相同,当频率小于临界频率ω0时旋转纵波θ波和横波S2波不存在,当频率大于临界频率ω0时,θ波和S2波的传播速度随频率增加而减小.     

横向各向同性多孔介质中的地震波传播

基于各向异性多孔介质中的广义Ｂｉｏｔ理论，导出了横向各向同性多孔介质中波传播的特征方程．指出在多孔介质中有４种类型的频散和耗散波传播：准纵波ＱＰ１（快纵波）、准纵波ＱＰ２（慢纵波）、准横波ＱＳＶ和横渡ＳＨ．文中给出了４种波速度的解析表达式．数值计算频率曲线和衰减曲线与Ｓｃｈｍｉｔｔ（１９８９）用均值处理得到的结果类似．还给出了波传播过程中３种类型准体波之间的耦合系数（或称转换系数）．     

流体饱和多孔介质黏弹性动力人工边界

基于Biot流体饱和多孔介质本构方程，采用平面波和远场散射波经验叠加来反映外行波传播，以经验参数反映人工边界外行波动的衰减和多角度透射特性。在人工边界处分别施加反映固相和液相介质传播效应的弹簧及阻尼来模拟人工边界以外的无限域介质对来自有限域的外行波的能量的吸收作用。从而形成一种流体饱和多孔介质的黏弹性动力人工边界。数值算例表明：边界的精度和稳定性高于现有的黏性边界、黏弹性人工边界及一阶透射边界。     

两相饱和介质中的集中力点源位移场解与应用

通过两相饱和介质Ｂｉｏｔ方程变换,利用势场分解较好地解决了饱和两相介质中Ｐ１和Ｐ２波的耦合问题．再由Ｐｏｉｓｓｏｎ方程和Ｈｅｌｍｈｏｔｚ方程的特性,求解得到两相饱和介质在集中力点源作用下的位移场Ｇｒｅｅｎ函数,进而通过阶跃函数和Ｆｏｕｒｉｅｒ逆变换,求得两相介质在集中力．作用下的波场．由上述结果,根据扩容进水模型,合理地解释了孕震前各主要阶段在地震记录中垂直向振幅与振幅比统计值的变化．最后结合工作实例,利用两相介质波场理论求得由一般弹性介质理论不易求得的骨架固体力学参数．     

各向异性介质中地震波前面的偏微分方程

从含２１个弹性参数的各向异性介质中关于位移分量ｕ_ｘ、ｕ_ｙ与ｕ_ｚ的偏微分波动方程组出发，通过假定平面波位移函数解，导出准Ｐ波、准ＳＶ波与准ＳＨ波的波前面偏微分控制方程，进而对各类特殊各向异性介质（横向各向同性介质、椭圆及立方体各向异性介质）中地震波前面偏微分方程进行了讨论．以上结果为研究各向异性介质中地震波传播规律以及进行正、反演研究奠定了理论基础．     

地下固体介质弹性模量反演

地下固体介质弹性模量是固体地球定量表征的重要参数,是探测地球内部结构、地下流体分布、设计合理工程方案的关键之一.本文首先简要分析常用的流体饱和孔隙介质岩石物理模型,在此基础上通过数值计算,详细讨论了流体饱和多孔介质等效弹性模量对固体基质、孔隙度、孔隙结构和孔隙流体的敏感性,探讨了利用等效介质弹性模量反演固体基质弹性模量的可行性,建立了固体基质弹性模量的非线性方程系统,提出了该方程系统的数值迭代求解方法,并通过对三类岩石样本实验室测量数据的反演和结果分析,验证了方法的有效性.文中同时通过不同条件下对实验数据的反演,探讨了孔隙结构、孔隙流体和等效介质弹性模量对反演效果的影响,为方法的合理有效应用提供依据.     

饱和多孔介质近场波动分析的一种黏弹性人工边界

采用有限模型数值方法求解能量开放系统中的波动问题时,虚拟人工边界的处理方式对计算结果的准确性和精度具有重要的影响.本文针对无限域饱和多孔介质中波传播问题的人工边界处理方式进行了研究,提出了饱和多孔介质近场波动分析的一种黏弹性人工边界处理方法.在考虑多孔介质中固相和液相的相互作用的情况下,通过在人工边界处分别施加反映固相和液相介质波传播效应的弹簧及阻尼来模拟饱和多孔介质中波的能量辐射效应影响.算例表明,本文建议的黏弹性人工边界具有较好的模拟效果.     

离散介质波场正演模拟与弱化性影响分析

从流变力学角度建立的离散介质本构关系同时考虑了介质的弹性、粘性与弱化性,与损伤力学建立的本构关系比较表明弱化因子具有损伤因子的力学意义。本文采用交错网格伪谱法正演模拟了离散介质中波的传播,并以平面波解分析了体波的频散和介质的吸收系数。高频和低频情况下波场数值模拟的结果是:饱和多孔介质中体波速度随弱化因子的增加而降低,介质吸收系数随弱化因子的增加而增加,弱化性对不同体波频散的影响程度不同。     

饱和多孔介质三维时域黏弹性人工边界与动力反应分析的显式有限元法

本文基于Biot的饱和多孔介质本构方程,考察具有辐射阻尼的外行球面波,推导了饱和多孔介质三维黏弹性人工边界的法向和切向边界方程;在已有的饱和多孔介质二维显式有限元数值计算方法基础上,提出该理论的三维方法,并开发了实现该三维方法的有限元程序.算例表明饱和多孔介质三维时域黏弹性人工边界与动力反应分析的显式有限元法具有较好的精度和稳定性.     

三种介质耦联系统动力反应分析的显式有限元法及其应用

在笔者已建立的流体饱和多孔介质动力分析的显式有限元法的基础上，提出了可分析任意形状的流体饱和多孔介质-单相弹性固体介质-理想流体介质耦联的复杂系统的动力响应的显式有限元方法．该方法建立的有限元方程列式具有解耦特征，不需求解联立方程组，因而极大地提高了计算效率．将这一方法用于分析了考虑库水、坝、淤泥层和基岩这一复杂系统动力相互作用问题的斜坝面的地震响应，并给出了一些计算结果．      

声波在两种多孔介质界面上的反射和透射

本文导出了声波在两种多孔介质界面上反射、透射的一般计算公式.作为例子,数值计算了P₁波入射于界面时,P₁、P₂和S波的反射、透射系数与声波频率、入射角等量之间的关系.结果表明,各种模式波的反射、透射系数与入射角、多孔介质性质有关,在Biot特征频率附近与频率有关,并用界面两侧的法向能流相等验证了结果的正确性.若把多孔介质当作均匀固体处理,将会得到显著不同的结果.     

Reflection and refraction of plane harmonic waves at an interface between elastic solid and porous solid saturated by viscous liquid

A general solution of Biot's field equations governing small motions of a porous solid saturated by viscous liquid is employed to study the reflection and refraction at the interface between an elastic solid and a liquid-saturated porous solid. The incident wave is assumed to be plane and homogeneous, propagating through the isotropic elastic solid. The poroelastic solid is considered to be a dissipative one. Amplitude and energy ratios are computed numerically for a particular model. With first-order corrections for the porosity of solid and viscosity of liquid, the limiting cases of low and high frequencies are computed.     

Moving load on a porous,liquid-saturated solid

Summary The object of this paper is to study the stresses produced in a porous liquid-saturated solid of the type considered byBiot [1]²) by a normal load moving along the surface of such a solid. Two cases have been considered. In the first case, the porous solid is taken to be semi-infinite, while in the second case we consider a layer of the liquid-saturated porous solid resting on a smooth rigid foundation. Expressions have been obtained for the stresses at any point in the medium due to a normal load moving along the free surface of the porous solid. Detailed numerical calculations have been carried out for liquid-saturated sandstone, using the data given byFatt [9] for such a medium. These calculations show that the normal stress zz in the solid falls off approximately as 1/z with increase in the depthz below the free surface, and that the stresses in the solid and in the liquid fall off rapidly as we move away from the point directly below the moving load.     

Analytical solutions for dynamic pressures of coupling fluid-solid-porous medium due to P wave incidence

Wave reflection and refraction in layered media is a topic closely related to seismology, acoustics, geophysics and earthquake engineering. Analytical solutions for wave reflection and refraction coefficients in multi-layered media subjected to P wave incidence from the elastic half-space are derived in terms of displacement potentials. The system is composed of ideal fluid, porous medium, and underlying elastic solid. By numerical examples, the effects of porous medium and the incident wave angle on the dynamic pressures of ideal fluid are analyzed. The results show that the existence of the porous medium, especially in the partially saturated case, may significantly affect the dynamic pressures of the overlying fluid.     

The effect of inertial coupling on seismic reflection amplitudes

A problem of reflection and transmission of elastic waves at a plane interface between a uniform elastic solid half-space and a porous elastic half-space containing two immiscible fluids is investigated. The theory developed by Lo, Sposito and Majer for porous media containing two immiscible fluids is employed to find out the reflection and transmission coefficients. The incident wave is assumed to propagate through the uniform elastic half-space and two cases are considered. In the first case, a beam of plane longitudinal wave is assumed to be incident and in the second case, a beam of transverse wave is assumed to be incident at the interface. By taking granite as impervious elastic medium and columbia fine sandy loam containing air-water mixture as porous medium, reflection and transmission coefficients are obtained. By neglecting the inertial coupling coefficients, these coefficients are reduced to those obtained by Tomar and Arora using the theory of Tuncay and Corapcioglu. It is found that the inertial coupling parameters significantly affect the phase speeds and the amplitude ratios of the transmitted waves.     

Surface wave propagation in a transversely isotropic elastic layer overlying a liquid saturated porous solid half-space and lying under the uniform layer of liquid

Dispersion of Rayleigh-type surface wave is studied in a homogeneous transversely isotropic elastic layer overlying a nondissipative liquid-saturated porous solid half-space and lying under a uniform layer of homogeneous liquid. The frequency equation in the form of ninth-order determinant is obtained.Special cases have been deduced by reducing the depth of the layers to zero and by changing the transverse isotropic layer to an isotropic layer. Dispersion curves for the phase velocity have been plotted for a particular model.     

Propagation of seismic waves in patchy-saturated porous media: double-porosity representation

Propagation of harmonic plane waves is studied in a patchy-saturated porous medium. Patchy distribution of the two immiscible fluids is considered in a porous frame with uniform skeletal properties. A composition of two types of patches, connected through continuous paths, constitutes a double-porosity medium. Different compressibilities of pore-fluids in two porous phases facilitate the wave-induced fluid-flow in this composite material. Constitutive relations are considered with frequency-dependent complex elastic coefficients, which define the dissipative behaviour of porous aggregate due to the flow of viscous fluid in connected patches. Relevant equations of motion are solved to explain the propagation of three compressional waves and one shear wave in patchy-saturated porous solids. A numerical example is solved to illustrate dispersion in phase velocity and quality factor of attenuated waves in patchy-saturated porous materials. Role of fluid–solid inertial coupling in Darcy's law is emphasized to keep a check on the dispersion of wave velocities in the porous composite. Effects of patchy saturation on phase velocities and quality factors of attenuation are analysed using the double-porosity formulation as well as the reduced single-porosity equivalents.     

Immiscible two-phase fluid flows in deformable porous media

Macroscopic differential equations of mass and momentum balance for two immiscible fluids in a deformable porous medium are derived in an Eulerian framework using the continuum theory of mixtures. After inclusion of constitutive relationships, the resulting momentum balance equations feature terms characterizing the coupling among the fluid phases and the solid matrix caused by their relative accelerations. These terms, which imply a number of interesting phenomena, do not appear in current hydrologic models of subsurface multiphase flow. Our equations of momentum balance are shown to reduce to the Berryman–Thigpen–Chen model of bulk elastic wave propagation through unsaturated porous media after simplification (e.g., isothermal conditions, neglect of gravity, etc.) and under the assumption of constant volume fractions and material densities. When specialized to the case of a porous medium containing a single fluid and an elastic solid, our momentum balance equations reduce to the well-known Biot model of poroelasticity. We also show that mass balance alone is sufficient to derive the Biot model stress–strain relations, provided that a closure condition for porosity change suggested by de la Cruz and Spanos is invoked. Finally, a relation between elastic parameters and inertial coupling coefficients is derived that permits the partial differential equations of the Biot model to be decoupled into a telegraph equation and a wave equation whose respective dependent variables are two different linear combinations of the dilatations of the solid and the fluid.     

Determining maximum shear stress in confined substrate from elastic wave reflection coefficient

The relationship between the maximum shear stress in a substrate solid and the elastic wave reflection coefficient from the interface between the substrate solid and an overlying solid half-space is investigated. Both substrate and overlying solid media are assumed to be initially isotropic and stress-free. Then as the substrate is subjected to horizontal confined stresses it becomes anisotropic. It is shown that longitudinal and shear wave reflection coefficients are related to the degree of stress induced anisotropy in the substrate medium. From this relation the confined stress level and the maximum shear stress generated on the vertical planes of the substrate are estimated. Authors in their previous investigation computed plane wave reflection coefficient in a biaxially compressed solid substrate immersed in a fluid. This paper reports for the first time how the maximum shear stress in a biaxially compressed substrate medium can be measured from the plane wave reflection coefficients when the overlying medium is also a solid half-space.