非饱和土中多相流动的试验研究和数值模拟

针对多孔介质中水、气和非水相流体的多相流动特点,建立了描述非水相流体污染物迁移问题的数学模型。采用离心模型试验和数值分析的方法模拟了土壤非饱和区中的多相流动过程,得到了污染物的时空分布特征和污染范围。模型试验和数值分析结果表明,轻非水相流体在地表泄漏后,会在重力作用下进入非饱和土体并向下迁移,部分滞留于土体孔隙中;到达地下水位时会浮在水面上并且继续侧向运移;水文地质条件对非饱和土中多相流动特征有重要的影响。     

各向异性双重孔隙介质的应力与油水两相渗流耦合理论模型

针对天然裂缝性油藏的特性,建立了描述双重孔隙介质中油水两相流体流动特性的流固耦合理论模型。该模型不仅考虑了渗透率的各向异性,而且考虑了岩石固体骨架变形的各向异性。渗流方程是依据双重孔隙的概念建立起来的,而固体骨架变形控制方程则是根据Biot 的等温、线性孔隙弹性理论建立起来的。同时,给出了横向各向同性及结构各向异性、固体材料各向同性时的双重孔隙介质的应力与油水两相渗流耦合理论模型。对该模型进行了简化,并将其简化后模型与单相流的各项同性和各向异性双重孔隙介质流固耦合理论模型进行了比较。     

双变量耦合作用对非饱和岩土波动特性的影响研究

为了研究双变量耦合效应对非饱和岩土波动特性的影响,假定固、液和气材料之间以及它们与骨架之间的力学特性均相互解耦。以Bishop平均应力和修正吸力为骨架的双应力变量,以骨架应变和饱和度为骨架的双应变变量,从小应变变形的多孔介质工程力学出发建立了非饱和多孔岩土的波动控制方程。利用不同双变量建立的线弹性本构方程相互一致的性质,建立了波动方程模型参数和常规室内试验土工参数之间的换算关系。新波动方程的刚度矩阵具有对称性,因而满足弹性力学互易定律。利用新波动方程获得了非饱和岩土三个压缩波和一个剪切波的波速计算公式。数值分析研究结果表明,双变量的耦合效应对剪切波波速无影响,对P2波和P3波的影响可以忽略不计。在饱和度较小时对P1波波速有明显影响。耦合效应越大,对P1波波速的影响越明显,但其影响程度随着饱和度的增大迅速减小。     

内水压作用下粘弹性饱和土-隧洞衬砌相互作用

混凝土衬砌既有粘弹性性质,又有渗透性。实际工程中内水压力值由衬砌和孔隙水共同承担,该文通过引入与孔隙流体体积分数有关的应力系数合理地分配了衬砌和孔隙水分别承担的内水压力值。根据衬砌和土体界面处衬砌中流体速度和土体中流体速度相等以及应力和位移连续性条件建立了部分透水边界条件。将衬砌和土体分别视为多孔粘弹性材料和液固两相介质,采用饱和多孔介质理论和粘弹性理论,在频率域内给出了内水压力作用下粘弹性饱和土-衬砌相互作用时饱和粘弹性土位移、应力和孔压和衬砌的位移和应力解析表达式。进行了参数研究,表明:应力系数以及衬砌和土体相对渗透系数对系统动力响应影响很大。另外,应力系数合理地确定了边界衬砌和孔隙水分别承担的内水压力值。     

含液饱和多孔二维梁的动力特性分析

基于线弹性理论和Biot多孔介质模型,分析了含液饱和多孔二维简支梁的动力响应,其中考虑了固体颗粒和流体的可压缩性以及孔隙流体的粘滞性。通过Fourier级数展开和常微分方程组的求解,得到了含液饱和多孔二维梁动力响应问题的解,并将其退化为单相固体二维梁的情形与Bernoulli-Euler梁和Timoshenko梁的自由振动相比较,验证了该文方法的正确性。作为数值算例,分析了含液饱和多孔二维梁的自由振动以及在均布简谐荷载作用下的动力响应特性,分析了表面渗透条件、孔隙流体渗透系数和荷载频率等参数对含液饱和多孔二维梁的自由振动频率、固相位移和孔隙流体压力等物理量的影响。     

流体饱和半空间中埋置球面P1、P2和SV波源动力格林函数

基于Biot流体饱和孔隙介质理论,采用Hankel积分变换方法,在频域内求解了流体饱和半空间中埋置球面P1、P2和SV波源的动力格林函数。首先由Hankel积分变换将空间域内球面波展开为波数域内柱面波的叠加;然后在半空间表面对称位置虚拟放置一同样大小的球面波源,这样对于球面膨胀波源(P1和P2波源),地表剪应力为零,但存在非零正应力和孔隙水压,对于球面剪切波源(SV波源),地表正应力和孔隙水压为零,但存在非零剪应力;最后叠加球面波源、虚拟波源和残余半空间表面应力产生的动力响应,即可求得流体饱和半空间中埋置球面波源波数域内的动力响应,空间域内埋置球面波源的动力格林影响函数则由Hankel逆变换求得。该文给出的球面波源动力格林函数,为建立以球面P1、P2和SV波动力格林函数为基本解的间接边界元方法,求解饱和多孔介质中三维轴对称弹性波散射问题奠定了基础。     

非饱和土地基的三维非轴对称动力响应

考虑土颗粒、孔隙流体的压缩性以及各相物质间的黏性、惯性耦合,采用Bishop有效应力公式和毛管压力函数的V-G模型,建立了非饱和土的动力控制方程.通过引入位移函数,并利用Cauchy-Reimann条件,在直角坐标系下将非饱和土的波动方程进行解耦,进而采用双重Fouricr变换,求得了位移和应力在变换域上的一般解.结合...     

饱和多孔介质一维瞬态波动问题的解析分析

采用基于混合物理论的多孔介质模型,提出了饱和多孔介质一维动力响应的初边值问题。利用拉氏变换和卷积定理,分别得到了边界自由排水时在任意应力边界条件和任意位移边界条件下瞬态波动过程的解析表达。几种典型的数值算例同时给出了两类边界条件下瞬态波动过程中多孔固体的位移场、应力场和孔隙流体的速度场、压力场。结果表明,饱和多孔介质的波动过程是多孔固体和孔隙流体中以同一速度传播的两种波动的耦合过程,时效特性分析也揭示了饱和多孔介质固有的表观粘弹性性质。     

饱和弹性裂隙介质的混合物理论

本文首先用损伤力学的方法,按孔隙的配置及几何结构,分别定义了含各向异性分布裂隙的固体介质的二阶连续法向裂纹张量和切向裂纹张量。然后,在裂隙内充满流体时,对组分速度、组分偏应力等混合物理论的基本变量进行了各向异性修正。并用混合物理论,建立了饱和裂隙介质中各组分的质量和动量平衡方程。最后,在仅考虑裂纹的单一张开度时,针对线弹性骨架材料,得到了由不可压缩材料构成的各组分的动力学控制方程。     

水饱和混凝土单轴压缩弹塑性损伤本构模型

多孔多相的饱和混凝土中,孔隙自由水对混凝土的力学特性有显著的影响。该文基于损伤力学基本原理建立了单轴压缩条件下水饱和混凝土的弹塑性损伤本构模型,并结合太沙基“有效应力原理”,认为材料的损伤是由本体有效应力和结构有效应力引起的,根据应力平衡条件得出了两种有效应力下的应力关系方程,并在此基础上建立了水饱和混凝土的单轴压缩损...     

Mathematical framework for unsaturated flow in the finite deformation range

The presence of fluid in the pores of a solid imposes a volume constraint on the deformation of the solid. Finite changes in the pore volume alter the degree of saturation of a porous material, impacting its fluid flow and water retention properties. This intricate interdependence between the hydromechanical properties related to solid deformation and fluid flow is amplified when the deformation of the solid matrix is large. In this paper, we present a mathematical framework for coupled solid‐deformation/fluid‐diffusion in unsaturated porous material considering geometric nonlinearity in the solid matrix. The framework relies on the continuum principle of thermodynamics to identify an effective or constitutive stress for the solid matrix, and a water‐retention law that highlights the interdependence of the degree of saturation, suction, and porosity of the material. Porous materials are typically heterogeneous, making them susceptible to localized deformation. In this work, we consider random heterogeneities in density and degree of saturation as triggers of localized deformation in a porous material. Copyright © 2013 John Wiley & Sons, Ltd.     

An efficient finite element procedure for analyzing three‐phase porous media based on the relaxed Picard method

Effective simulation of the solid‐liquid‐gas coupling effect in unsaturated porous media is of great significance in many diverse areas. Because of the strongly nonlinear characteristics of the fully coupled formulations for the three‐phase porous media, an effective numerical solution scheme, such as the finite element method with an efficient iterative algorithm, has to be employed. In this paper, an efficient finite element procedure based on the adaptive relaxed Picard method is developed for analyzing the coupled solid‐liquid‐gas interactions in porous media. The coupled model and the finite element analysis procedure are implemented into a computer code PorousH2M, and the proposed procedure is validated through comparing the numerical simulations with the experimental benchmarks. It is shown that the adaptive relaxed Picard method has salient advantage over the traditional one with respect to both the efficiency and the robustness, especially for the case of relatively large time step sizes. Compared with the Newton‐Raphson scheme, the Picard method successfully avoids the unphysical ‘spurious unloading’ phenomenon under the plastic deformation condition, although the latter shows a better convergence rate. The proposed procedure provides an important reference for analyzing the fully coupled problems related to the multi‐phase, multi‐field coupling in porous media. Copyright © 2014 John Wiley & Sons, Ltd.     

An effective stress based numerical model for hydro-mechanical analysis in unsaturated porous media

 A fully coupled flow-deformation model is presented for the behaviour of unsaturated porous media. The governing equations are derived based on the equations of equilibrium, effective stress concept, Darcy's law, Henry's law, and the conservation of fluid mass. Macroscopic coupling between the flow and deformation fields is established through the effective stress parameters. The microscopic link between the volumetric deformations of the two pore system (i.e. the pore-air and the pore-water) is established using Betti's reciprocal theorem. Both links are essential for a proper modelling of flow and deformation in unsaturated porous media. The discretised form of the governing equations is obtained using the finite element technique. As application of the model, experimental results from several laboratory tests reported in the literature are modelled numerically. Good agreement is obtained between the numerical and the experimental results in all cases.     

Transport and fate of volatile organic chemicals in unsaturated, nonisothermal, salty porous media: 1. Theoretical development.

A wide variety of volatile organic chemicals (VOC) have been applied to agricultural land or buried in chemical waste sites. The fate of these chemicals depends upon several mechanisms such as sorption, degradation, and transport in liquid and gaseous phases. Understanding the transport mechanisms affecting the volatile chemicals can lead to better management strategies. A theory describing inorganic solute transport, water and heat transfer, and the fate and transport of VOC in porous media has been developed. This theory includes matric water pressure head, solution osmotic pressure head, gravity pressure head, temperature, inorganic solute concentration, and VOC concentration gradients as driving forces for heat and mass transfer. The effect of surface tension, as a function of VOC concentration and temperature, on the matric water pressure head is included. The VOC can be associated with gas, liquid, and solid phases of the porous media. The gas and liquid phases are mobile, but the solid phase is immobile. The transfer of VOC across the gas/liquid, liquid/solid, and gas/solid interfaces is included using sorption-equilibrium assumptions at the interfaces. The VOC can degrade. This degradation is described by a first-order decay rate. The theory can be used to predict spatial and temporal variations of water content, temperature, inorganic concentration and the total concentration of VOC within a porous medium. The concentration of VOC in each phase can be predicted also.     

平衡饱和度差异性产生机理及其对非饱和土力学特性的影响

通过双孔隙结构分析结果确定在同一基质吸力下的试样将因孔隙分布的随机性而表现出不同的平衡饱和度, 进一步通过理想非饱和土的水气分布确定饱和度差异将影响非饱和土的力学性质研究. 采用压力板仪与直剪仪的简化组合试验对上述理论分析结果进行验证, 研究结果表明:平衡饱和度差异存在并随着基质吸力的增大而逐渐减小;在同一基质吸力下试样的抗剪强度随平衡饱和度的增加而降低;进一步的拟合结果显示平衡饱和度对与基质吸力相关的内摩擦角影响显著;通过对试验数据及其平均值的研究建议在最小与最大基质吸力下进行多次平行试验, 可以在不显著增加试验时间的同时减小平衡饱和度差异的影响.     

An extended finite element method for fluid flow in partially saturated porous media with weak discontinuities; the convergence analysis of local enrichment strategies

In this paper, a numerical model is developed for the fully coupled analysis of deforming porous media containing weak discontinuities which interact with the flow of two immiscible, compressible wetting and non-wetting pore fluids. The governing equations involving the coupled solid skeleton deformation and two-phase fluid flow in partially saturated porous media are derived within the framework of the generalized Biot theory. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three-phase formulation. The other variables are incorporated into the model via the experimentally determined functions that specify the relationship between the hydraulic properties of the porous medium, i.e. saturation, permeability and capillary pressure. The spatial discretization by making use of the extended finite element method (XFEM) and the time domain discretization by employing the generalized Newmark scheme yield the final system of fully coupled non-linear equations, which is solved using an iterative solution procedure. Numerical convergence analysis is carried out to study the approximation error and convergence rate of several enrichment strategies for bimaterial multiphase problems exhibiting a weak discontinuity in the displacement field across the material interface. It is confirmed that the problems which arise in the blending elements can have a significant effect on the accuracy and convergence rate of the solution.     

Analytical decoupling of poroelasticity equations for acoustic-wave propagation and attenuation in a porous medium containing two immiscible fluids

Poroelasticity theory has become an effective and accurate approach to analyzing the intricate mechanical behavior of a porous medium containing two immiscible fluids, a system encountered in many subsurface engineering applications. However, the resulting partial differential equations in the theory intrinsically take on a coupled form in the terms pertinent to inertial drag, viscous damping, and applied stress, making it difficult to obtain closed-form, steady-state analytical solutions to boundary-value problems except in special cases. In the present paper, we demonstrate that, for dilatational wave excitations, these partial differential equations can be decoupled analytically into three Helmholtz equations featuring complex-valued, frequency-dependent normal coordinates that correspond physically to three independent modes of dilatational wave motion. The normal coordinates in turn can be expressed in the frequency domain as three different linear combinations of the solid dilatation and the linearized increment of fluid content for each pore fluid, or equivalently, as three different linear combinations of total dilatational stress and two pore fluid pressures. These representations are applicable to strain-controlled and stress-prescribed boundary conditions, respectively. Numerical calculations confirm that the phase speed and attenuation coefficient of the three dilatational waves represented by the Helmholtz equations are exactly identical to those obtained previously by numerical solution of the dispersion relations for dilatational wave excitation of a porous medium containing two immiscible fluids. Thus, dilatational wave motions in unsaturated porous media subject to suitable boundary conditions can now be accurately modeled analytically.     

A formulation for an unsaturated porous medium undergoing large inelastic strains

 This paper presents a formulation for a saturated and partially saturated porous medium undergoing large elastic or elastoplastic strains. The porous material is treated as a multiphase continuum with the pores of the solid skeleton filled by water and air, this last one at constant pressure. This pressure may either be the atmospheric pressure or the cavitation pressure. The governing equations at macroscopic level are derived in a spatial and a material setting. Solid grains and water are assumed to be incompressible at the microscopic level. The isotropic elastoplastic behaviour of the solid skeleton is described by the multiplicative decomposition of the deformation gradient into an elastic and a plastic part. The effective stress state is limited by the Drucker-Prager yield surface, for which a particular “apex formulation” is advocated. The water is assumed to obey Darcy's law. Numerical examples of strain localisation of dense and loose sand conclude the paper. Received 15 March 2001     

Mechanics of porous elastic materials containing multiphase fluid

A continuum theory of mixtures for a porous elastic solid saturated by immiscible viscous fluids is presented. The theory includes micro-inertial effects for the local fluctuation in volume fractions of the solid and fluid constituents. Gradients of volume fraction of both the elastic solid and fluid constituents are included in the constitutive variables. Equations governing the macroscopic motion are developed and show that the present theory contains both Biot's equations and multiphase Darcy flow through porous media as special cases.     

恒压下树脂在双尺度多孔介质中的流动特性

基于复合材料液态模塑(LCM)工艺过程中存在半饱和区域的实验现象以及对预制体双尺度效应的逐步认识, 一些学者提出用沉浸模型来研究双尺度多孔介质的不饱和流动。通过体积均匀化方法描述了双尺度多孔介质复合材料液态模塑工艺模型的特征, 得到含有沉浸项的双尺度多孔介质的质量守恒方程, 并采用有限元法对方程进行数值求解, 通过具体算例计算了考虑双尺度效应时恒压树脂注射下不同时段的压力分布状态, 得到树脂在填充过程中流动前沿半饱和区域从出现到消失的过程, 采用不同注射压力进行模拟并比较。结果表明, 与单尺度多孔介质模型不同, 双尺度多孔介质模型更能反映实际树脂填充过程中出现的半饱和区域现象。