不可压饱和粘弹性多孔介质固结问题的Gurtin型变分原理

基于多孔介质理论,在固相骨架和孔隙流体微观不可压,固相骨架小变形且满足线性粘弹性积分型本构关系的假定下,利用卷积积分的性质,本文首先建立了以固相骨架位移、孔隙流体相对速度和孔隙流体压力为宗量的流体饱和粘弹性多孔介质固结问题的一个Gurtin型变分原理.其次,利用Lagrange乘子法解除相关的变分约束条件,建立了流体饱和粘弹性多孔介质固结问题的若干广义Gurtin型变分原理,包括第三类的Hu-Washizu型变分原理.最后,简单讨论了等价初边值问题的相应变分原理.这些Gurtin型变分原理的建立不仅丰富了饱和粘弹性多孔介质的相关理论,而且为相关数值模拟方法,如有限元法、无网格法等的建立奠定了理论基础.     

流体饱和两相多孔介质拟静态问题的有限元解法

给出基于混合物理论的流体饱和两相多孔介质模型,该模型由一可变形固体 一流体相组成。采用Ｇａｌｅｒｋｉｎ加权残值法导出求解拟静态问题的有限元公式,并编制了二维有限元程序。用程序分析了一维和二维问题,得到合理的结果。     

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.     

Diffusion of Randon in Porous Media Saturated with Gels and Emulsions

The effective diffusion coefficient of radon was determined in polymer/silicate gels and clay suspension used as sealing materials in environmental protection. On the basis of the experimental findings, it was concluded that both materials drastically decrease the convective mass transport in porous media. Simultaneously, the effective diffusion coefficient was reduced significantly. Thus, the radon flux might be decreased by 5 to 6 orders of magnitude in porous systems originally having gas or low water saturation by injection of gel-forming materials or placement of clay suspensions. At high water saturation, however, the diffusion transport of radon can be slightly restricted in consolidated and unconsolidated porous media. The laboratory studies may firmly allow us to conclude that hydrogels and clay suspensions are prospective candidates in an integrated environmental technology to be used for restriction of radon migration in subsurface regions.     

Acoustics of Rotating Deformable Saturated Porous Media

We investigate wave propagation in elastic porous media which are saturated by incompressible viscous Newtonian fluids when the porous media are in rotation with respect to a Galilean frame. The model is obtained by upscaling the flow at the pore scale. We use the method of multiple scale expansions which gives rigorously the macroscopic behaviour without any prerequisite on the form of the macroscopic equations. For Kibel numbers A A(1), the acoustic filtration law resembles a Darcys law, but with a conductivity which depends on the wave frequency and on the angular velocity. The bulk momentum balance shows new inertial terms which account for the convective and Coriolis accelerations. Three dispersive waves are pointed out. An investigation in the inertial flow regime shows that the two pseudo-dilatational waves have a cut-off frequency.     

Wave Dynamics of Saturated Porous Media and Evolutionary Equations

Nonlinear wave dynamics of an elastically deformed saturated porous media is investigated following the Biot approach. Mathematical models under research are the Biot model and its generalization by consideration of viscous stresses inside liquids. Using two-scales and linear WKB methods, the classical Biot system is transformed to a first-order wave equation. To construct the solution of the other system, an asymptotic modified two-scales method is developed. Initial system of equations is transformed to a nonlinear generalized Korteweg–de Vries–Burgers equation for quick elastic wave. Distinctions of wave propagation in the context of the Biot model and its generalization are shown.     

轴对称热-力埋置载荷下半空间饱和孔隙介质的动力响应

基于修正的Biot热弹性本构理论,得到了饱和多孔介质热-力耦合的动力学控制方程.针对半空间孔隙介质在内置简谐热-力轴对称载荷作用下的动力问题,利用Hankel变换获得了响应的解析表达式,并利用Han-kel逆变换进行数值求解,分析了埋置深度、表面热边界条件等对响应的影响规律.结果表明:孔隙水压力在载荷作用处上方有负压出现;环向、径向及竖向应力在载荷作用处发生突变,且在载荷作用处上方均出现拉应力;在载荷作用处下方,孔隙水压力及竖向、径向和环向应力均随着深度的增大而减小.当内置热载荷仅设置温差,而无外热源输入时,温差对孔隙介质中的响应几乎不产生影响.当孔隙介质表面绝热时,孔隙水压力小于表面等温情况下的值.     

Radon Emanation in Partially Saturated Porous Media

Radon emanation which is the fraction of radon-222 atoms released in the connected pore space of a porous material, increases when the water content increases because of the low recoil range of this atom in water compared with air. This complex phenomenon is studied using reconstructed porous media and random packings where the phase distribution is obtained by a lattice Boltzmann technique incorporating interfacial tension and wetting. The influence of the pore structure, of the recoil range and of saturation, is systematically studied. The numerical results are in good agreement with data from uranium mine tailings.     

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.     

饱和不可压正交各向异性多孔弹性板的动力弯曲分析

基于多孔介质理论,在Kirchhoff直法线假定以及小变形和线性本构关系前提下,建立了饱和不可压正交各向异性多孔弹性板的线性动力分析模型.针对流体的面内扩散问题,在忽略面内惯性项的影响下,进一步简化了分析模型,给出了相应的基本控制方程以及初始和边界条件的一般描述.根据所建立的模型,采用Fourier级数展开法研究了四边简支透水正交各向异性矩形多孔弹性板在冲击载荷作用下的拟静态和动力弯曲响应,数值分析了不同参数下孔隙流体压力等效弯矩、固相有效应力等效弯矩以及挠度的变化规律和动力特征.研究表明在外载荷作用初始阶段,孔隙流体对板弯曲变形的影响不可忽视.     

Stress Generated During Drying of Saturated Porous Media

The article is a contribution for the modelling of heat and mass transfers coupled to strain–stress equations during drying of deformable two-phase media. Both unidirectional and bidirectional configurations are examined. In order to compare the results, one assumes the material of a convectively dried clay slab in two configurations. Numerical calculations of the temperature, drying curves variations and the spatio-temporal distributions of moisture, temperature and drying induced stresses are evaluated. A significant difference was observed between the results obtained for both configurations particularly in intensity of the shear stress that caused cracking.     

Dispersion and Dispersivity Tensors in Saturated Porous Media with Uniaxial Symmetry

The coefficient of dispersion, D _ij , and the dispersivity, a _ijkl , appear in the expression for the flux of a solute in saturated flow through porous media. We present a detailed analysis of these tensors in an axially symmetric porous medium, e.g., a stratified porous medium, with alternating layers, and show that in such a medium, the dispersivity is governed by six independent moduli. We present also the constraints that have to be satisfied by these moduli. We also show that at least two independent experiments are required in order to obtain the values of these coefficients for any three-dimensional porous medium domain.     

Hydromechanical Modelling of Experimentally Compacted Saturated Argillaceous Porous Media

In order to model the experimental compaction of clays as completely as possible, it is necessary to use the hydromechanical coupled three-dimensional theory for saturated porous media. The proposed formulation is based on elastoplasticity, more precisely on modified Cam-clay model. The identification of the parameters of the model is made by special oedometric experiments at steady state. The compaction experiments are simulated with accuracy in transient and steady states and complement those obtained in a recent study based only on steady state.     

横观各向同性饱和多孔半空间与梁的动力相互作用

通过引入三个标量函数,结合Fourier变换,首先将横观各向同性饱和多孔半空间的基本方程组简化为一个6阶控制方程和一个2阶控制方程;求解这两个控制方程,给出了横观各向同性饱和多孔半空间相关物理量的解析表达式.利用带扩展项的正弦级数解答,在将梁下地基表面沉降也展成正弦级数后,结合板-地基的相容条件(连续条件),对横观各向同性饱和多孔半空间与有限长梁的动力相互作用问题进行了分析、计算.另外,利用Fourier变换,对横观各向同性饱和多孔半空间与无限长梁的动力相互作用问题进行了分析.     

Osmotic Mechanism of Fracture Growth in Saturated Porous Media

Fracture growth in saturated porous bodies under the action of the osmotic pressure developed in the fracture by a solute for which the fracture surface represents a semipermeable membrane is considered. This mechanism of fracture growth, which follows directly from the basic laws of fracture mechanics and physical chemistry, should be a fairly general effect of significance in a number of geochemical and technological processes. In particular, the role of osmosis in well flushing and cementing processes was noted in study by N. G. Avetisyan, Choice of type of drill solution for drilling in unstable rocks, published in: Review Information. Drilling [in Russian], VNIIOENG (1983) and the mechanism was briefly discussed in monograph by A. Kh. Mirzadzhanzade and V. M. Entov, Drilling Hydrodynamics [in Russian], Nedra, Moscow (1985).In study by R. V. Gol'dshtein, V. M. Entov, and B. P. Pavlovskii, Model of the development of hydrogen fractures in metal, Dokl. Acad. Nauk SSSR, Vol. 237, 828 (1977) a comparable mathematical model was proposed for explaining the hydrogen embrittlement of metals. Finally, in study by J. P. Sargent and K. H. G. Ashbee, The contribution of osmosis to dimensional instability of adhesive joints, J. Adhesion, Vol. 17, 83 (1984) a very similar mechanism of fracture development in polymeric materials due to the osmotic splitting of internal joints as a result of the release in the joints of a substance dissolved in the solid polymer was discussed and visual observation data were given.The property of semipermeability of the fracture surface (permeability for water and impermeability for dissolved salts), which is fundamental to our study, is taken as a basic hypothesis and will not discussed in what follows. Many arguments could be advanced to show that natural semipermeable membranes can develop in rocks, especially in argillaceous ones. However, these arguments are not definite and clearly lie beyond the competence of the authors whose task is to trace the possible mechanical consequences of the presence of semipermeable membranes and draw them to the attention of the specialists.     

Thermodynamic Correction for Salts in Variably Saturated Porous Media

Using thermodynamic principles, the general relationship describing the equilibrium vapor content in the gas phase above a saline liquid and across a curved liquid–gas interface is developed. Since high salt concentration affects the intensive and extensive liquid properties, it is also necessary to account for these effects in liquid water content/liquid water pressure relationship curves so that experimentally derived curves for pure water may be useful for elevated salt concentrations. The appropriate thermodynamic relationships are derived to describe the salt effects on liquid and vapor properties. The resulting equations are valid for salt concentrations between zero and saturation, and for any temperatures that nominally occur in nearsurface geologic materials.     

Asymptotic Research of Nonlinear Wave Processes in Saturated Porous Media

The problem of nonlinear wave dynamics of a fluid-saturated porous medium is investigated. The mathematical model proposed is based on the classical Frenkel--Biot--Nikolaevskiy theory concerning elastic wave propagation and includes mass, momentum, energy conservation laws, as well as rheological and thermodynamic relations. The model describes nonlinear, dispersive, and dissipative medium. To solve the system of differential equations, an asymptotic modified two-scales method is developed and a Cauchy problem for initial equations system is transformed to a Cauchy problem for nonlinear generalized Korteweg--de Vries--Burgers equation for modulated quick wave amplitudes and an inhomogeneous set of equations for slow background motion. Stationary solutions of the derived evolutionary equation that have been constructed numerically reflect different regimes of elastic wave attenuation: diffusive, oscillating, and soliton-like.     

Three-Dimensional Analytical Models for Virus Transport in Saturated Porous Media

Analytical models for virus transport in saturated, homogeneous porous media are developed. The models account for three-dimensional dispersion in a uniform flow field, and first-order inactivation of suspended and deposited viruses with different inactivation rate coefficients. Virus deposition onto solid particles is described by two different processes: nonequilibrium adsorption which is applicable to viruses behaving as solutes; and colloid filtration which is applicable to viruses behaving as colloids. The governing virus transport equations are solved analytically by employing Laplace/Fourier transform techniques. Instantaneous and continuous/periodic virus loadings from a point source are examined.