一维流体饱和粘弹性多孔介质层的动力响应

本文研究了不可压流体饱和粘弹性多孔介质层的一维动力响应问题。基于粘弹性理论和多孔介质理论,在流相和固相微观不可压、固相骨架服从粘弹性积分型本构关系和小变形的假定下,建立了不可压流体饱和粘弹性多孔介质层一维动力响应的数学模型,利用Laplace变换,求得了原初边值问题在变换空间中的解析解,并利用Laplace逆变换的Crump数值反演方法,得到原动力响应问题的数值解。数值研究了饱和标准线性粘弹性多孔介质层的动力响应,分析了固相位移、渗流速度、孔隙压力及固相有效应力等的响应特征。结果表明,与不可压流体饱和弹性多孔介质相同,不可压流体饱和粘弹性多孔介质中亦只存在一个纵波,并且固相骨架的粘性对动力行为有显著的影响。     

Equations of the mechanics of porous media saturated with liquid and gas

The approach proposed by Podil'chuk [1] is used to derive a system of equations of motion for saturated porous media, allowance being made for the mutual influence of the solid, liquid, and gas phases. The permeabilities of the anisotropic porous medium are assumed to depend on the direction. It is shown that when there are no gas phases and the liquid is incompressible the system of equations reduces to the general equations of the theory of elasticity of an anisotropic body with fictitious stress components. For a porous medium saturated with liquid, the relationships between the permeabilities and the anisotropy constants are obtained. The motion of liquid in an elastic porous medium in the form of an orthotropic cylindrical region with a cavity in the form of a circular cylinder is considered as an example.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 82–87, July–August, 1981.     

Saturated Compressible and Incompressible Porous Solids: Macro- and Micromechanical Approaches

In this paper two complementary approaches are used to describe the mechanical behavior of saturated compressible and incompressible porous solids. The macroscopic investigation is based on the mixture theory, restricted by the volume fraction concept. In the micromechanical approach, a hierarchy of conditionally ensemble averaged fluid and solid phase momentum balance equations are derived for a simple model of quasi-static liquid saturated porous media. The ensemble averaged equations for both the phases agree remarkably well with the macroscopic results. A micromechanical basis for Terzhagi's effective stress concept is presented. In addition, an expression for additional partial solid stress modifying the effective stress principle, to account for deformability of solid materials, is also derived.     

Thermo-Chemo-Electro-Mechanical Formulation of Saturated Charged Porous Solids

A thermo-chemo-electro-mechanical formulation of quasi-static finite deformation of swelling incompressible porous media is derived from a mixture theory including the volume fraction concept. The model consists of an electrically charged porous solid saturated with an ionic solution. Incompressible deformation is assumed. The mixture as a whole is assumed locally electroneutral. Different constituents following different kinematic paths are defined: solid, fluid, anions, cations and neutral solutes. Balance laws are derived for each constituent and for the mixture as a whole. A Lagrangian form of the second law of thermodynamics for incompressible porous media is used to derive the constitutive restrictions of the medium. The material properties are shown to be contained in one strain energy function and a matrix of frictional tensors. A principle of reversibility results from the constitutive restrictions. Existing theories of swelling media should be evaluated with respect to this principle.     

基于介观结构的饱和与非饱和多孔介质有效应力

基于描述含液颗粒材料介观结构的Voronoi 胞元模型和离散颗粒集合体与多孔连续体间的介-宏观均匀化过程, 定义饱和与非饱和多孔介质有效应力. 导出了计及孔隙液压引起之颗粒体积变形的饱和多孔介质广义有效应力. 用以定义广义有效应力的Biot 系数不仅依赖于颗粒材料的多孔连续体固体骨架及单个固体颗粒的体积模量(材料参数),同时与固体骨架当前平均广义有效应力及单个固体颗粒的体积应变(状态量) 有关. 提出了描述非饱和多孔介质中非混和固体颗粒、孔隙液体和气体等三相相互作用的具介观结构的Voronoi 胞元模型.具体考虑在低饱和度下双联(binary bond) 模式的摆动(pendular) 液桥系统介观结构. 导出了基于介观水力-力学模型的非饱和多孔介质的各向异性有效应力张量与有效压力张量. 考虑非饱和多孔介质Voronoi 胞元模型介观结构的各向同性情况,得到了与非饱和多孔连续体理论中唯象地假定的标量有效压力相同的有效压力形式.但本文定义的与确定非饱和多孔介质有效应力和有效压力相关联的Bishop 参数由基于三相介观水力-力学模型, 作为饱和度、孔隙度和介观结构参数的函数导出,而非唯象假定.      

Saturated Elastic Porous Solids: Incompressible,Compressible and Hybrid Binary Models

Constitutive models for a general binary elastic-porous media are investigated by two complementary approaches. These models include both constituents treated as compressible/incompressible, a compressible solid phase with an incompressible fluid phase (hybrid model of first type), and an incompressible solid phase with a compressible fluid phase (hybrid model of second type). The macroscopic continuum mechanical approach uses evaluation of entropy inequality with the saturation condition always considered as a constraint. This constraint leads to an interface pressure acting in both constituents. Two constitutive equations for the interface pressure, one for each phase, are identified, thus closing the set of field equations. The micromechanical approach shows that the results of Didwania and de Boer can be easily extended to general binary porous media.     

Elastic Waves in Swelling Porous Media

Time harmonic waves in a swelling porous elastic medium of infinite extent and consisting of solid, liquid and gas phases have been studied. Employing Eringen’s theory of swelling porous media, it has been shown that there exist three dilatational and two shear waves propagating with distinct velocities. The velocities of these waves are found to be frequency dependent and complex valued, showing that the waves are attenuating in nature. Here, the appearance of an additional shear wave is new and arises due to swelling phenomena of the medium, which disappears in the absence of swelling. The reflection phenomenon of an incident dilatational wave from a stress-free plane boundary of a porous elastic half-space has been investigated for two types of boundary surfaces: (i) surface having open pores and (ii) surface having sealed pores. Using appropriate boundary conditions for these boundary surfaces, the equations giving the reflection coefficients corresponding to various reflected waves are presented. Numerical computations are performed for a specific model consisting of sandstone, water and carbon dioxide as solid, liquid and gas phases, respectively, of the porous medium. The variations of phase speeds and their corresponding attenuation coefficients are depicted against frequency parameter for all the existing waves. The variations of reflection coefficients and corresponding energy ratios against the angle of incidence are also computed and depicted graphically. It has been shown that in a limiting case, Eringen’s theory of swelling porous media reduces to Tuncay and Corapcioglu theory of porous media containing two immiscible fluids. The various numerical results under these two theories have been compared graphically.     

垂直下降管中两相流的流型以及液相粘度对流型的影响

对空气－油在垂直下降管中的流型进行了实验研究，采用的管径为２９ｍｍ，油和空气的折算流速分别达到４ｍ／ｓ和２０ｍ／ｓ，并借助于压降脉动分析和目测观察相结合的方法来进行流型的识别。研究表明，油气两相流的流型不同于低粘液体的两相流流动，通过实验研究并结合前人的研究成果，给出了液相粘度对流型转变的影响趋势。     

A Local Model for the Energy Transfer in a Saturated Static Mixture

In the present work the transient energy transfer in a nonsaturated porous medium is studied, using a mixture theory viewpoint. The porous matrix is assumed homogeneous, rigid and isotropic, while the fluid is a Newtonian incompressible one and both are assumed static. Since the homogeneous matrix is not saturated, gradients of concentration are present. The porous medium and the fluid (a liquid) will be regarded as continuous constituents of a mixture that will have also a third constituent, an inert gas, assumed with zero mass density and thermal conductivity. The problem is described by a set of two partial differential equations which represent the energy balances for the fluid and the solid constituents. Isovalues for these two constituents are plotted, considering representative time instants and selected values for the energy equations coefficients and for the saturation.     

Fundamental Solution of the System of Equations of Steady Oscillations in the Theory of Fluid-Saturated Porous Media

In the present paper the linear theory of the liquid-saturated porous medium consisting of a microscopically incompressible solid skeleton containing microscopically incompressible liquid is considered. The fundamental solution of the system of linear coupled partial differential equations of the steady oscillations of the porous solids is constructed in terms of elementary functions and some basic properties are established.     

Exact solutions to one-dimensional transient response of incompressible fluid-saturated single-layer porous media

Based on the Biot theory of porous media,the exact solutions to onedimensional transient response of incompressible saturated single-layer porous media under four types of boundary conditions are developed.In the procedure,a relation between the solid displacement u and the relative displacement w is derived,and the well-posed initial conditions and boundary conditions are proposed.The derivation of the solution for one type of boundary condition is then illustrated in detail.The exact solutions for the other three types of boundary conditions are given directly.The propagation of the compressional wave is investigated through numerical examples.It is verified that only one type of compressional wave exists in the incompressible saturated porous media.     

GURTIN VARIATIONAL PRINCIPLE AND FINITE ELEMENT SIMULATION FOR DYNAMICAL PROBLEMS OF FLUID-SATURATED POROUS MEDIA

Based on the theory of porous media,a general Gurtin variational principle for theinitial boundary value problem of dynamical response of fluid-saturated elastic porous media isdeveloped by assuming infinitesimal deformation and incompressible constituents of the solid andfluid phase.The finite element formulation based on this variational principle is also derived.Asthe functional of the variational principle is a spatial integral of the convolution formulation,thegeneral finite element discretization in space results in symmetrical differential-integral equationsin the time domain.In some situations,the differential-integral equations can be reduced to sym-metrical differential equations and,as a numerical example,it is employed to analyze the reflectionof one-dimensional longitudinal wave in a fluid-saturated porous solid.The numerical results canprovide further understanding of the wave propagation in porous media.     

On mechanics of saturated granular materials

A continuum theory of saturated granular materials is formulated. The basic balance laws for the solid phase as well as for the fluid phase are presented. The constitutive equations are derived and the basic equations of motion of the solid and fluid continua are obtained. Several cases of interest, such as incompressible granules saturated with liquids are discussed. It is shown that the theory contains, as its special cases, the Mohr-Coulomb criterion for a granular material as well as Darcy's law of flow through porous media.     

An elastoplasticity model in porous media theories

In this article, porous media theories are referred to as mixture theories extended by the well-known concept of volume fractions. This approach implies the diverse field functions of both the porous solid matrix and the pore fluid to be represented by average functions of the macroscale.The present investigations are based on a binary model of incompressible constituents, solid skeleton, and pore liquid, where, in the constitutive range, use is made of the second-grade character of general heterogeneous media. Within the framework of geometrically finite theories, the paper offers a set of constitutive equations for the solid matrix, the viscous pore liquid and the different interactions between the constituents. The constitutive model applies to saturated as well as to empty solid materials, taking into account the physical nonlinearities based on elasto-plastic solid deformations. In particular, the constitutive model concentrates on granular materials like soil or concrete, where the elastic deformations are usually small and the plastic range is governed by kinematically hardening properties.     

Water removal from porous media by gas injection: experiments and simulation

The flow of a saturated gas through a porous medium, partially occupied by a liquid phase, causes evaporation due to gas expansion. This process, referred to as flow-through drying, is important in a wide variety of natural and industrial applications, such as natural gas production, convective drying of paper, catalysts, fuel cells and membranes. X-ray imaging experiments were performed to study the flow-through drying of water-saturated porous media during gas injection. The results show that the liquid saturation profile and the rate of drying are dependent on the viscous pressure drop, the state of saturation of the gas and the capillary characteristics of the porous medium. During the injection of a completely saturated gas, drying occurs only due to gas expansion. Capillary-driven flow from regions of high saturation to regions of low saturation lead to more uniform saturation profiles. During the injection of a dry gas, a drying front develops at the inlet and propagates through the porous medium. The experimental results are compared with numerical results from a continuum model. A good agreement is found for the case of sandstone. The comparison is less satisfactory for the experiments with limestone.     

饱和土地基在简谐荷载作用下的解析分析

基于多孔介质混合物理论,用解析的方法研究了不可压饱和土地基受到简谐荷载作用下的动力响应问题。利用Fourier积分变换求解耦合方程组,得到了二维饱和土介质在简谐荷载作用下的通解。针对表面透水的具有下卧基岩的饱和土层以及半无限饱和土地基的边界条件,获得了固体骨架位移、孔隙流体位移、固体骨架有效应力以及孔隙流体压力的积分形式解答,并通过数值算例分析了饱和土地基在简谐荷载作用下的响应。     

Propagation of acceleration waves in incompressible saturated porous solids

Within the framework of the incompressible porous media model, the propagation properties of acceleration waves in liquid-filled porous solids is discussed. The incompressibility of the two constituents in the model forces the amplitudes of the longitudinal waves in the skeleton and in the liquid to satisfy a certain relation. The two propagation speeds are presented by examination for the existence of acceleration waves and only longitudinal and transverse waves are realizable in the incompressible two-phase porous materials.