含液各向异性多孔介质应变局部化分析

工程中的含液多孔介质如饱和或非饱和岩土材料往往具有各向异性特性。采用Rudnicki建立的针对岩土材料的各向异性本构模型,对轴对称压缩试验中的含液多孔介质骨架的各向异性力学行为进行了分析;基于不连续分叉理论,导出了静态非渗流条件下处于轴对称应力状态的含液多孔介质应变局部化发生的临界模量、剪切带方向以及不连续速度矢量的显式表达式,在此基础上计算并讨论了材料参数变化和孔隙液体存在对各向异性多孔介质应变局部化的影响。     

分数导数模型描述的饱和土桩纵向振动分析

土体具有黏弹性性质,为了更好地考虑饱和土体固相土骨架的黏弹性性质,在分数导数理论和多孔介质理论的基础上,将土体视为液固饱和两相介质,并利用分数导数模型来描述饱和土固相土骨架的应力-应变关系,建立分数导数模型描述的饱和土的控制方程。在三维轴对称情况下,利用势函数和分离变量法研究了分数导数模型描述的饱和土中桩的振动问题。分析了模型参数对饱和土中桩的竖向振动的影响。研究表明,分数导数模型描述的饱和土的控制方程应用范围更广,模型参数对桩的竖向振动有较大的影响。     

土质边坡的饱和−非饱和渗流分析及特殊应力修正

基于连续多孔介质原理与混合体原理引入流?固耦合模型,采用FISH语言编制程序,建立了初始渗流场设置函数、饱和?非饱和渗流分析模块、特殊应力修正模块以及非饱和单元抗剪强度修正模块,实现了利用FLAC3D进行饱和?非饱和渗流分析,同时基于饱和?非饱和渗流场修正非饱和区土体单元的有效应力以及抗剪强度,完成了将FLAC3D中饱和土流?固耦合计算原理扩展到非饱和土中。在二次开发的分析模块基础上对Liakopoulos砂柱排水试验进行数值模拟,验证了计算模型和计算程序的正确性。同时也研究了降雨入渗对土质边坡的渗流场、位移场以及稳定性演变过程的影响,揭示了降雨诱发边坡失稳的机制。     

一种适用于孔隙体积应变的有效应力方程

土力学奠基石Terzaghi有效应力原理被广泛应用于油藏孔隙和渗透率应力敏感研究中,然而其对于岩石孔隙体积应变的适用性存在争议。对颗粒不可压缩和颗粒可压缩的多孔介质分别进行了受力分析,推导了总体积、颗粒骨架、孔隙体积的有效应力表达式,与Biot、Skepmton有效应力方程对比,建立了适用于孔隙体积应变的新型有效应力方程,并进行了试验论证和应用举例。研究表明:在颗粒不可压缩多孔介质中,有效应力为超出平衡孔隙流压之外的颗粒间宏观等效应力;在颗粒可压缩变形多孔介质中,有效应力为其相同应变下的等效应力,有3种有效应力分别适用于总体积应变、颗粒体积应变、孔隙体积应变;新提出的孔隙体积有效应力方程与孔隙度、岩石总体积压缩系数、颗粒压缩系数、总应力和流压相关,4个理论计算式计算结果在3种多孔介质试验测试结果中的偏差均在5%以内;孔隙体积有效应力系数解决了如何定量增总应力来等效模拟储层降流压生产过程这一关键问题,3个压缩系数关系式理论计算准确方便。     

简谐线源荷载作用下热流固耦合地基的动力响应

基于Biot波动理论和广义热弹性理论,对简谐线源荷载（力荷载和热荷载）作用下的热-流-固耦合地基的动力响应问题进行了研究。将地基看成是均质各向同性、完全饱和的多孔半空间介质,利用无量纲化和Fourier变换方法对热-流-固耦合控制方程进行简化,得到了变换域内应力分量、位移分量、温度分布及超孔隙水压力的一般解,并利用Fourier逆变换得到了相应的积分形式解答。通过数值计算对按热-流-固耦合理论、饱和多孔弹性理论和热弹性理论得到的结果进行了比较,同时分析了热-流-固耦合条件下热荷载激振频率对竖向应力、竖向位移、温度分布以及超孔隙水压力的影响。     

饱和多孔介质动力应变局部化分析中的内尺度律

对饱和多孔介质动力应变局部化分析中的材料内尺度律问题进行研究，讨论了当软化发生时饱和多孔介质分析的动力学稳定性问题，研究工作表明，由于液体相的作用，饱和多孔材料的动力学特性与单相固体材料有着明显的不同，特别是当应变局部化发生时，在特定情况下将仍存在可通过材料软化区域的动力波，也就是波动问题仍具有弥散特性，在此基础上，给出多孔材料的内尺度律的判定公式，讨论了内尺度律存在的条件。     

渗流的PFC-CFD耦合细观数值模拟

本文针对饱和多孔介质中渗流特点,在分析渗流连续介质力学模型的基础上,采用描述多孔介质中固相颗粒和液相流体耦合的细观力学模型,其中固相颗粒采用离散元的颗粒流理论(PFC)模拟,液相流体通过求解平均Navier-Stokes方程的计算流体动力学(CFD)技术计算,并利用建议的模型对二维渗流问题进行了模拟验证。数值模拟结果表明,采用PFC-CFD耦合细观力学模型能够描述从低雷诺流到高雷诺流范围很大的流体运动,可以用于多孔介质中的渗流问题分析。     

广义平面应力条件下径向渗流的液固耦合

考虑了多孔介质渗透率随孔隙变化的特点,建立了基本方程;对于广义平面应力条件下的径向渗流问题,提出了解耦方法,并求出了耦合条件下的孔隙压力及介质应力、应变、位移的解析解。实例计算表明,耦合效应不容忽略。      

基于三维数字图像相关技术的砂岩渗流-应力耦合变形局部化特性试验研究

为研究渗流-应力耦合作用下砂岩变形局部化破坏特征,将三维数字图像相关（three-dimensionaldigitalimage correlation,简称3D-DIC）技术运用于可视化三轴伺服控制试验系统中,对砂岩开展了不同渗透水压条件下的三轴压缩试验研究。研究结果表明：（1）在渗流-应力耦合作用下,砂岩表面变形场云图经历了从均匀到非均匀的演化过程。在峰前的变形较为均匀,在峰值处出现应变集中,在峰后较短时间内迅速形成变形局部化带;（2）随着渗透水压的增大,岩石的峰值强度、弹性模量呈现指数型非线性衰减,峰值强度弱化系数和弹性模量弱化系数均增大,且渗透率逐渐增大,最大渗透率出现的时间点越早;（3）随着渗透水压的增大,砂岩变形局部化带从剪切状过渡到张拉-剪切状,轴向和径向变形局部化带带内外应变在峰后短时间内出现较大差异,且带内应变远大于带外应变;（4）随着渗透水压的增大,砂岩变形局部化启动应力水平越高,启动的时刻点越早。渗透水压与砂岩变形局部化启动应力水平呈线性相关性,轴向变形局部化启动水平受渗透水压的影响比径向更为显著。     

结构性黄土二元介质本构模型在局部化剪切带中的应用

基于破损力学理论,将结构性黄土抽象成具有一定结构强度的结构块和摩擦带组成的二元介质模型。对结构性黄土体来说,局部化剪切带问题也是土体的破损问题,剪切带萌生发展的实质就是结构块向摩擦带转化的动态过程。应用结构性土的双参数破损率二元介质本构模型,采用数值分析方法模拟了平面应变压缩条件下结构性土中局部化剪切带萌生、扩展的过程,研究了不同缺陷方案下局部化剪切带的形态、特性与规律,发现结构性土中局部化剪切带的发展起初是由一段段不连续的微小局部破坏区域在外荷载逐步作用下渐进扩展连接贯通而形成整体剪切带的破坏形式。二元介质本构模型和常规有限元的结合,形象生动地再现了局部化剪切带萌生、发展的过程。     

饱和多孔介质中水力-力学-传质耦合过程的混合有限元法

对饱和多孔介质提出了一个含溶混污染物输运（传质）过程的混合元方法,其中污染物输运过程数学模型包含了对流、机械逸散、分子弥散和吸附等机制。固相位移、应变和有效应力,孔隙水压力、压力空间梯度和Darcy速度,污染物浓度、浓度空间梯度和浓度流量在单元内均为独立变量分别插值。基于胡海昌-Washizu三变量广义变分原理,结合可以滤掉虚假振荡的特征线方法,推导出饱和土中水力-力学-传质耦合问题控制方程的单元弱形式,并导出了混合元计算公式。数值模拟证明了所提出的方法可以提供与传统4点积分方案同样精度,同时能够提高计算效率。     

A numerical model for nonlinear large deformation dynamic analysis of unsaturated porous media including hydraulic hysteresis

A numerical model based on the theory of mixtures is proposed for the nonlinear dynamic analysis of flow and deformation in unsaturated porous media. Starting from the conservation laws, the governing differential equations and the finite element incremental approximations suitable for nonlinear large deformation static and dynamic analyses are derived within the updated Lagrangian framework. The coupling between solid and fluid phases is enforced according to the effective stress principle taking suction dependency of the effective stress parameter into account. The effect of hydraulic hysteresis on the effective stress parameter and soil water characteristic curve is also taken into account. The application of the approach is demonstrated through numerical analyses of several fundamental nonlinear problems and the results are compared to the relevant analytical solutions. The effects of suction, large deformations and hydraulic hysteresis on static and dynamic response of unsaturated soils are particularly emphasized.     

Multiphase SPH modeling of free surface flow in porous media with variable porosity

This paper presents a numerical model for simulating free surface flow in porous media with spatially varying porosity. The governing equations are based on the mixture theory. The resistance forces between solid and fluid is assumed to be nonlinear. A multiphase SPH approach is presented to solve the governing equations. In the multiphase SPH, water is modeled as a weakly compressible fluid, and solid phase is discretized by fixed solid particles carrying information of porosity. The model is validated by several numerical examples including seepage through specimen, fast flow through rockfill dam and wave interaction with porous structure. Good agreements between numerical results and experimental data are obtained in terms of flow rate and evolution of free surface. Parameter study shows that (1) the nonlinear resistance law provides more accurate results; (2) particle size and porosity have significant influence on the porous flow.     

Solid–liquid–air coupling in multiphase porous media

This paper addresses various issues concerning the modelling of solid–liquid–air coupling in multiphase porous media with an application to unsaturated soils. General considerations based on thermodynamics permit the derivation and discussion of the general form of field equations; two cases are considered: a three phase porous material with solid, liquid and gas, and a two phase porous material with solid, liquid and empty space. Emphasis is placed on the presentation of differences in the formulation and on the role of the gas phase. The finite element method is used for the discrete approximation of the partial differential equations governing the problem. The two formulations are then analysed with respect to a documented drainage experiment carried out by the authors. The merits and shortcomings of the two approaches are shown. Copyright © 2003 John Wiley & Sons, Ltd.     

Work input for unsaturated soils considering interfacial effects

In this research, the interfacial energy is taken into account in the deformation work for unsaturated soils. Based on porous media theory, the thermodynamic balance equations for each phase and the interface are used to derive the work input for unsaturated soils. The work input equation serves as the basis and starting point for the choice of stress state variables, based on which the conjugate stresses and strain increments are derived. The influences of the interfaces on the effective stress and the constitutive law for the liquid phase are then discussed based on the work input equation. The effective stress can be expressed as Bishop's type, and the effective stress parameter is shown to be a function of both the degree of saturation and the interfacial area. The constitutive law for the liquid phase under dynamic condition is also presented. The relationship among interfacial area, saturation, and capillary pressure is proposed to calculate the value of the effective stress. Experimental data obtained from literature are used to validate the proposed model equations. Results show that our findings are in accordance with the existing research. Unlike the phenomenal study, our research has a rigorous theoretical basis, which lays a foundation for further research of unsaturated soils considering the interfacial effects.     

基于梯度塑性模型的多孔介质应变局部化分析的基本理论

讨论了引入梯度塑性模型情况下的含液多孔介质双重内尺度律的特征以及相互作用问题。在引入梯度塑性本构模型的情况下,一方面材料应变局部化分析数值结果的正则性得到保证;而另一方面,含液多孔介质会出现双重内尺度律参数的共同作用问题。本文给出了此时内尺度律预测的一个基本方法,并对稳定性问题进行了分析,讨论了不同情况下实波速存在的条件,给出了对于给定的渗透系数情况下实波速存在的波数区间,并对相关现象进行了解释。     

考虑孔隙变形的孔隙介质本构关系初探

孔隙存在是孔隙介质材料结构的本质特征,它决定了孔隙介质的本构关系呈现更为复杂的性质。首先给出了孔隙介质的视应力、视应变、骨架实际应力和骨架实际应变的定义,并在理想孔隙介质的物质模型假定下讨论了理想孔隙介质的本构关系,表明即使孔隙介质的骨架结构满足虎克弹性体本构关系的假定,即假定骨架的实际应力与实际应变之间呈现线性关系,但由于孔隙的存在,孔隙介质的视应力与视应变之间还是呈现非线性,说明应力与变形之间的非线性是孔隙介质的固有特性。     

单层非饱和多孔介质一维瞬态响应半解析解

基于Zienkiewicz提出的非饱和多孔介质波动理论,考虑两相流体和固体颗粒的压缩性以及惯性、黏滞和机械耦合作用,采用半解析的方法获得了一类典型边界条件下单层非饱和多孔介质一维瞬态响应解。首先推导出无量纲化后以位移表示的控制方程,并将其写成矩阵形式;然后,将边界条件齐次化,求解控制方程所对应的特征值问题,得到了满足齐次边界条件的特征值和相对应的特征函数。根据变异系数法并利用特征函数的正交性,得到了一系列仅黏滞耦合的关于时间的二阶常微分方程及相应的初始条件。在此基础上,运用精细时程积分法给出了常微分方程组的数值解。最后,通过若干算例验证了结果的正确性并探讨了单层非饱和多孔介质一维瞬态动力响应的特点。该方法可推广应用于其他典型的边界条件。     

The effective stress concept and the evaluation of changes in pore air pressure under jacketed isotropic compression tests for dry sand based on the 2‐phase porous theory

The effective stress concept for solid‐fluid 2‐phase media was revisited in this work. In particular, the effects of the compressibility of both the pore fluid and the soil particles were studied under 3 different conditions, i.e., undrained, drained, and unjacketed conditions based on a Biot‐type theory for 2‐phase porous media. It was confirmed that Terzaghi effective stress holds at the moment when soil grains are assumed to be incompressible and when the compressibility of the pore fluid is small enough compared to that of the soil skeleton. Then, isotropic compression tests for dry sand under undrained conditions were conducted within the triaxial apparatus in which the changes in the pore air pressure could be measured. The ratio of the increment in the cell pressure to the increment in the pore air pressure, m, corresponds to the inverse of the B value by Bishop and was obtained during the step loading of the cell pressure. In addition, the m values were evaluated by comparing them with theoretically obtained values based on the solid‐fluid 2‐phase mixture theory. The experimental m values were close to the theoretical values, as they were in the range of approximately 40 to 185, depending on the cell pressure. Finally, it was found that the soil material with a highly compressible pore fluid, such as air, must be analyzed with the multi‐phase porous mixture theory. However, Terzaghi effective stress is practically applicable when the compressibilities of both the soil particles and the pore fluid are small enough compared to that of the soil skeleton.