Mimetic Finite Difference Methods for Diffusion Equations

This paper reviews and extends the theory and application of mimetic finite difference methods for the solution of diffusion problems in strongly heterogeneous anisotropic materials. These difference operators satisfy the fundamental identities, conservation laws and theorems of vector and tensor calculus on nonorthogonal, nonsmooth, structured and unstructured computational grids. We provide explicit approximations for equations in two dimensions with discontinuous anisotropic diffusion tensors. We mention the similarities and differences between the new methods and mixed finite element or hybrid mixed finite element methods.     

Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method

A finite element algorithm for frictionless contact problems in a two‐phase saturated porous medium, considering finite deformation and inertia effects, has been formulated and implemented in a finite element programme. The mechanical behaviour of the saturated porous medium is predicted using mixture theory, which models the dynamic advection of fluids through a fully saturated porous solid matrix. The resulting mixed formulation predicts all field variables including the solid displacement, pore fluid pressure and Darcy velocity of the pore fluid. The contact constraints arising from the requirement for continuity of the contact traction, as well as the fluid flow across the contact interface, are enforced using a penalty approach that is regularised with an augmented Lagrangian method. The contact formulation is based on a mortar segment‐to‐segment scheme that allows the interpolation functions of the contact elements to be of order N. The main thrust of this paper is therefore how to deal with contact interfaces in problems that involve both dynamics and consolidation and possibly large deformations of porous media. The numerical algorithm is first verified using several illustrative examples. This algorithm is then employed to solve a pipe‐seabed interaction problem, involving large deformations and dynamic effects, and the results of the analysis are also compared with those obtained using a node‐to‐segment contact algorithm. The results of this study indicate that the proposed method is able to solve the highly nonlinear problem of dynamic soil–structure interaction when coupled with pore water pressures and Darcy velocity. Copyright © 2015 John Wiley & Sons, Ltd.     

基于CT三维重建与逆向工程技术的煤体数字模型的建立

为了建立能够表征煤体真实孔隙结构的数字模型,进而进行数值模拟研究,通过μCT225kVFCB高精度CT系统扫描得到了大柳塔煤矿长焰煤CT数据,可观测到的最小孔隙直径为1.94 μm。使用基于Matlab语言的三维重建程序结合逆向工程技术,提出了一种将煤体CT三维数据转换为CAD数字模型的方法。以Ansys建立的煤体有限元模型为例,对煤体瓦斯渗流进行了模拟,分析了煤体孔隙内的速度及压力分布规律,并计算了沿X、Y、Z方向的渗透系数。计算结果表明：在微观尺度下（< 100 μm）煤体渗透系数呈现各向异性,其受煤体结构的影响较明显。提出的基于CT三维重建结合逆向工程技术构建的煤体CAD数字模型不仅可进行有限元分析,同时也可以被EDEM等离散元分析软件所使用,拓宽了煤体CT三维数据的应用范围,丰富了煤体在微观尺度上的研究方法。     

不同应力路径下超固结黏土试样变形局部化分析

基于改进伏斯列夫面超固结黏土三维本构模型,利用有限元软件ABAQUS材料子程序接口,采用回映应力更新算法,实现了该模型在有限元分析中的应用。通过该模型与比奥固结理论的耦合,对超固结比为8的超固结黏土在三轴压缩、三轴伸长及平面应变应力条件下的变形局部化问题,进行了水-土耦合弹塑性有限元分析。分析结果表明：剪切带带内、带外点经历不同应力路径;剪切带带外单元经历了体缩、剪胀及被吸水体缩过程,而剪切带带内单元一直保持剪胀趋势;剪切带的形成伴随着剪胀,剪切带内、外出现了负的孔压,且孔压的分布也具有局部化特性。关于剪切带带内、外的孔隙水压及体变变化趋势与剪切速率有关,而平面应变介于三轴压缩与三轴伸长之间,但平面应变较早出现剪切带。孔隙水的迁移速度影响剪切带带内单元的剪胀,进而影响剪切带的形成及发展;而围压和弱单元位置也对剪切带的形成也有影响。     

复杂储层多尺度数字岩石评价

复杂储层岩石矿物组成非均质性强,孔喉结构细小.储集空间有效性评价、岩石结构精细评价及流体赋存状态与运移规律评价是决定复杂储层油气勘探成效的关键.针对复杂储层的储集空间（孔喉、裂缝）、岩石结构（矿物、有机质）、流体特征3方面,建立了复杂储层多尺度数字岩石评价技术及工作流程.储集空间表征方面:二维大面积分析技术可建立跨越6~7个数量级的多尺度选取及非均质性评价;多尺度CT及FIB-SEM联用可精确刻画孔喉和裂缝的三维空间分布;电化学和显影剂技术可以有效地帮助分析微观孔隙连通性.固体组分分析方面:XRF及Qemscan联用可定量评价矿物组成与分布;三维FIB-SEM技术可以实现有机质形态和分布的定量分析.流体特性方面:荷电效应可用于微量残留有机流体的识别与表征;通过合成孔径、润湿性、表面微结构均可调控的纳米材料,开展地层条件下页岩油赋存及流动物理模拟研究,确定了单一因素对页岩油赋存及可动孔径下限的影响;利用分子模拟研究油气在无机、有机质纳米孔隙中的聚集机理与扩散潜力.复杂储层多尺度数字岩石评价技术体系和一系列具体应用可以有效地填补常规储层分析手段的不足,为页岩油气、致密砂岩油气储层以及深部油气储层等复杂储层有效性评价和含油气性定量评价提供技术支撑.      

A multiscale DEM-LBM analysis on permeability evolutions inside a dilatant shear band

This paper presents a multiscale analysis of a dilatant shear band using a three-dimensional discrete element method and a lattice Boltzmann/finite element hybrid scheme. In particular, three-dimensional simple shear tests are conducted via the discrete element method. A spatial homogenization is performed to recover the macroscopic stress from the micro-mechanical force chains. The pore geometries of the shear band and host matrix are quantitatively evaluated through morphology analyses and lattice Boltzmann/finite element flow simulations. Results from the discrete element simulations imply that grain sliding and rotation occur predominately with the shear band. These granular motions lead to dilation of pore space inside the shear band and increases in local permeability. While considerable anisotropy in the contact fabric is observed with the shear band, anisotropy of the permeability is, at most, modest in the assemblies composed of spherical grains.     

Elastic stress and strain in jointed rock masses by means of crack tensor analysis

Summary An elastic stress-strain relation is formulated in terms of crack tensors which makes it possible to take into account explicitly the effect of joints on elastic behavior of rock masses. The present study is to discuss some related topics which may be encountered in its practical application. Two problems are solved by incorporating the elastic stress-strain relation into a program for three-dimensional finite element analyses; i. e., stress concentration by surface loading and displacement by excavation of an intersecting tunnel. Validity of the results is checked by comparing them with a laboratory model test and a field test, with the following conclusions: The overall distribution of stress definitely depends on a joint stiffness ratio (i. e., normal stiffness to shear stiffness). If the ratio is chosen as unity, the stress concentration occurs mainly in the direction parallel to major joints. If the ratio is high, say 10, then the stress concentrates along the perpendicular as well as the parallel directions to major joints. It can be said, on the basis of the fairly good agreement of the calculations using the high stiffness ratio with the field and laboratory measurements, that the elastic solution by crack tensors provides a practical tool for estimating the stress and strain in strongly jointed rock masses.     

裂隙岩体三维柔度张量的数值试验方法

在裂隙岩体二维柔度张量数值试验的基础上,建立了裂隙岩体三维柔度张量及其表征单元体积（REV）尺度研究的简化数值试验方法。首先根据岩体裂隙的统计参数及分布规律,运用蒙特卡罗方法在研究域内获得与实际岩体裂隙同分布的三维随机裂隙网络,提取位于不同方位的岩体试件,运用二维柔度张量的数值试验方法求出各个平面方向上的二维柔度张量,然后根据二维与三维柔度张量的拓扑关系,用数学方法求解裂隙岩体的三维柔度张量。对于含3组正交全贯通裂隙的岩体,通过数值试验获得的柔度张量与理论解相比,其主对角线上各参数的误差在5%以内,表明该数值试验方法较为可靠。最后将此方法运用到小湾水电站工程中,确定左岸坝区裂隙岩体的应力REV为11 m×11 m×11 m,并获得该区域裂隙岩体的三维柔度张量。     

Characteristics of pore migration controlled by diffusion through the pore-filling fluid

We analyze drag and drop of pores filled with a fluid phase, e.g., water or melt, in which the constituting elements of the solid matrix are dissolved. Assuming that the diffusion through the fluid-phase dominates bulk transport kinetics, we address the problem of pore motion and calculate the pore mobility and the critical velocity of elongated and lenticular pores on a grain boundary for arbitrary dihedral angle. The found variations in critical velocity and mobility with dihedral angle are modest for given volume of pores with the two considered geometries. For given pore size, however, the dependence on dihedral angle accounts for several orders of magnitude in pore mobility and critical velocity.     

Evaluation of Containment Performance from Viewpoints of Diffusion and Dispersion for Impervious Structures at Coastal Landfill Sites

The containment performance of impervious structures is considered the most important performance, which the toxic substances are enclosed in coastal landfill sites. The containment performance is evaluated generally by the hydraulic conductivity and the thickness of impervious structures to focus on an advection. However, the leakage of toxic substances is affected by a diffusion and a dispersion. The diffusion and the dispersion are considered to be easily distinguished on the impervious structure which has the low-hydraulic conductivity. Such phenomena should be considered due to evaluate the containment performance. This is because to improve the containment performance and comprehend leakage of the toxic substances. The containment performance is evaluated from the viewpoint of the diffusion and the dispersion in this research. Concretely, the influence which the toxic substances leaks from impervious structures on the diffusion and the dispersion is evaluated by the infiltration and advection–dispersion analysis on steel-made side impervious walls. In other word, The relation between the leaking amount of toxic substances and coefficient of molecular diffusion, the relation between the travel time or the flow velocity and the leaking amount and the change in the water-level difference are considered respectively. So, the leaking amount which is influenced by a diffusion and a dispersion is considered. Consideration about to secure the containment performance of impervious structure which is restrained leakage by a diffusion and a dispersion.     

层状可压缩岩基三维固结问题的状态空间解

采用状态空间法求解层状可压缩岩基的三维固结问题。首先从直角坐标系下考虑可压缩性的三维Biot固结问题的控制方程出发,通过Laplace-Fourier变换得到状态空间方程,解此方程并通过Cayley-Hamilton定理,得到单层可压缩岩基三维固结问题的传递矩阵;然后利用传递矩阵法,结合层间连续性条件和边界条件,得到了层状可压缩岩基三维固结问题在积分变换域内的解答;最后应用Laplace-Fourier逆变换技术,得到层状可压缩岩基三维固结问题在物理域内的理论解答。编制了相应的计算程序,进行了数值计算与分析,证明了压缩性对岩基固结问题的影响     

Hydro-micromechanical modeling of wave propagation in saturated granular crystals

Biot theory predicts wave velocities in a saturated granular medium using the pore geometry, viscosity, densities, and elastic moduli of the solid skeleton and pore fluid, neglecting the interaction between constituent particles and local flow, which becomes essential as the wavelength decreases. Here, a hydro-micromechanical model, for direct numerical simulations of wave propagation in saturated granular media, is implemented by two-way coupling the lattice Boltzmann method (LBM) and the discrete element method (DEM), which resolve the pore-scale hydrodynamics and intergranular behavior, respectively. The coupling scheme is benchmarked with the terminal velocity of a single sphere settling in a fluid. In order to mimic a small amplitude pressure wave entering a saturated granular medium, an oscillating pressure boundary on the fluid is implemented and benchmarked with the one-dimensional wave equation. The effects of input waveforms and frequencies on the dispersion relations in 3D saturated poroelastic media are investigated with granular face-centered-cubic crystals. Finally, the pressure and shear wave velocities predicted by the numerical model at various effective confining pressures are found to be in excellent agreement with Biot analytical solutions, including his prediction for slow compressional waves.     

一种基于单元局部坐标系求解二维孔隙渗流问题的数值方法

将数值计算区域用三角形单元进行离散,并为每个单元构建局部坐标系。局部坐标系的X轴为三角形单元某一条边的方向,局部坐标系的原点为该边的其中一个端点。在局部坐标系下,基于“格林公式”及达西定律推导了单元压力梯度及单元流速的解析表达式,给出了流经单元各棱及各节点的流量计算方法。形成了类似固体弹簧系统的渗流管道网络,建立了管道压差与流量的函数关系。将各单元局部坐标系下求得的流速及流量转换至整体坐标系,并在节点上进行凝聚。通过引入流体体积模量实现了节点渗透压力的显式求解,通过引入节点饱和度实现了非饱和问题的求解。基于局部坐标系的方法具有物理意义明确、求解过程简单等特点。通过在局部坐标系下构建管道压差与管道流量的对应关系,将有限元的渗透刚度矩阵简化为两个管道的渗透刚度值,从而节省了内存,提高了计算效率。4个数值算例的计算结果与理论解基本一致,表明了该方法在求解稳态、非稳态、饱和、非饱和渗流问题时的精度。     

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。     

地浸场地残余溶液对水环境影响中的水文地球化学问题讨论

溶质迁移的理论是水环境评价及其整治的科学基础。溶质迁移理论包括水动力弥散、分子扩散和水文地球化学的水岩作用。文章讨论了地浸场地残留溶液对环境影响的预测方法、围岩对污染水的自净和地下水环境恢复的功能，对三种预测污染水对环境影响方法的计算蛄果进行了对比。通过以上讨论，展示水文地球化学在水环境评价和整治工作中有不可忽略的作用和意义，并提出了在水环境评价和整治工作中正确确定弥散系数、阻滞系数、饱和阻留容量、阻滞速率、溶质迁移速度的重要性。文中通过实例介绍了饱和阻滞容量、阻滞速率、溶质迁移速度等参数的求测计算方法。     

饱和冻土中弹性波的传播特性

用混合物连续介质理论,考虑了土颗粒骨架、冰、水三相介质,选取土颗粒位移、孔隙水位移、孔隙水压和孔隙冰压为基本变量,采用Bishop有效应力原理,建立了饱和冻土多孔介质的弹性波弥散方程。经理论推导,给出了饱和冻土中弹性波的传播速度及衰减的解析表达式。通过数值算例,探讨了饱和冻土中两种压缩波（Pl波和P2波）及剪切波（S波）的波速和衰减与频率和孔隙率、含冰量等土参数的关系。通过参数分析研究了饱和冻土中3种体波的传播特性。     

A self-adapting model for assessing hazardous environmental releases

Simulation results are presented by using an h-adaptive mass consistent finite element method (FEM) coupled with a Lagrangian particle transport technique (LPT) for dispersion associated with hazardous atmospheric releases. A three-dimensional wind field is first constructed from the adaptive FEM model. Lagrangian particles that define the contaminant dispersion are then produced with the LPT scheme, employing a random walk/stochastic approach. The application of FEM permits flow patterns with irregular geometries to be easily simulated, while the LPT permits contaminant particle dispersion patterns to be quickly depicted. The hybrid model is fast, runs on PCs, and appears well suited for emergency response dispersion predictions and assessment.     

基于GIS的孔隙含水层系统三维空间离散方法研究

分析了目前孔隙地下水流三维有限差分数值模拟中对含水层系统三维空间离散存在的问题，针对自然界孔隙含水层与隔水层空间分布的不连续性与厚度的不均匀性，研究了基于GIS的孔隙含水层系统三维空间离散实现的技术路线，提出了基于GIS与不规则六面体元的孔隙含水层系统的三维空间离散方法，最大限度地保证了离散体元中含水层类型的单一性，提高了孔隙地下水流模拟模型三维空间离散的精度。     

基于饱水页岩地震频段岩石物理测试的地震响应频散特征分析

页岩储层由于骨架和孔隙结构的微观非均质性,能够在地震频段内引起波诱导的孔隙流体流动相关的弹性频散和衰减,但声波测井和实验室超声实验测量频率段远超地震频段,不可避免产生测量速度和衰减差异。这里基于澳大利亚惠灵顿地区的页岩岩心在干燥和水饱和条件下地震频段的弹性和衰减测量结果,考虑频变反透射系数和衰减对地震波反射的影响,针对不同层厚的页岩储层开展地震响应计算,并利用Wigner-Ville分布时频分析技术讨论了页岩频散、衰减性质及层厚对其地震响应规律的作用。对于无明显速度频散和衰减的页岩储层,顶、底反射振幅的频变属性受调谐效应控制,主要呈现出低频异常和陷频特征;而对于速度频散和衰减强烈的储层,顶、底反射振幅的频变属性同时受到调谐效应与储层本身频散衰减性质的作用。干燥和含水页岩储层地震响应的频变性质差异有助于加深对含流体页岩地震响应特征的理解,而基于地震频段实测数据正演和时频分析技术,对于提高页岩的地震勘探精度和流体识别具有重要的作用。     

Three-Dimensional Modeling of Mass Transfer in Porous Media Using the Mixed Hybrid Finite Elements and the Random-Walk Methods

A three-dimensional (3D) mass transport numerical model is presented. The code is based on a particle tracking technique: the random-walk method, which is based on the analogy between the advection–dispersion equation and the Fokker–Planck equation. The velocity field is calculated by the mixed hybrid finite element formulation of the flow equation. A new efficient method is developed to handle the dissimilarity between Fokker–Planck equation and advection–dispersion equation to avoid accumulation of particles in low dispersive regions. A comparison made on a layered aquifer example between this method and other algorithms commonly used, shows the efficiency of the new method. The code is validated by a simulation of a 3D tracer transport experiment performed on a laboratory model. It represents a heterogeneous aquifer of about 6-m length, 1-m width, and 1-m depth. The porous medium is made of three different sorts of sand. Sodium chloride is used as a tracer. Comparisons between simulated and measured values, with and without the presented method, also proves the accuracy of the new algorithm.