Bridging Effective Stress and Soil Water Retention Equations in Deforming Unsaturated Porous Media: A Thermodynamic Approach

The finite deformation of an unsaturated porous medium is analysed from first principles of mixture theory. An expression for Bishop’s effective stress is derived from (1) the deformation-dependent Brooks and Corey’s water retention curve and (2) the restrictions on the constitutive relationships of an unsaturated medium subject to finite deformation. The resulting expression for the effective stress parameter \(\chi \) is reasonably consistent with experimental data from the literature. Hence, it is shown that Bishop’s equation is constitutively linked to water retention curves in deforming media.     

Equilibrium of Phases with Interfacial Energy: A Variational Approach

The paper proves the existence of equilibrium two phase states with elastic solid bulk phases and deformation dependent interfacial energy. The states are pairs (y,E) consisting of the deformation y on the body and the region E occupied by one of the phases in the reference configuration. The bulk energies of the two phases are polyconvex functions representing two wells of the substance. The interfacial energy is interface polyconvex. The last notion is introduced and discussed below, together with the interface quasiconvexity and interface null Lagrangians. The constitutive theory and equilibrium theory of the interface are discussed in detail under appropriate smoothness hypotheses. Various forms of the interfacial stress relations for the standard and configurational (Eshelby) interfacial stresses are established. The equilibrium equations are derived by a variational argument emphasizing the roles of outer and inner variations.     

A Quasilinear Based Procedure for Saturated/Unsaturated Water Movement in Soils

The quasilinear form of Richards equation for one-dimensional unsaturated flow in soils can be readily solved for a wide variety of conditions. However, it cannot explain saturated/unsaturated flow and the constant diffusivity assumption, used to linearise the transient quasilinear equation, can introduce significant error. This paper presents a quasi-analytical solution to transient saturated/unsaturated flow based on the quasilinear equation, with saturated flow explained by a transformed Darcy's equation. The procedure presented is based on the modified finite analytic method. With this approach, the problem domain is divided into elements, with the element equations being solutions to a constant coefficient form of the governing partial differential equation. While the element equations are based on a constant diffusivity assumption, transient diffusivity behaviour is incorporated by time stepping. Profile heterogeneity can be incorporated into the procedure by allowing flow properties to vary from element to element. Two procedures are presented for the temporal solution; a Laplace transform procedure and a finite difference scheme. An advantage of the Laplace transform procedure is the ability to incorporate transient boundary condition behaviour directly into the analytical solutions. The scheme is shown to work well for two different flow problems, for three soil types. The technique presented can yield results of high accuracy if the spatial discretisation is sufficient, or alternatively can produce approximate solutions with low computational overheads by using large sized elements. Error was shown to be stable, linearly related to element size.     

Upscaling of the Coupling of Hydromechanical and Thermal Processes in a Quasi-static Poroelastic Medium

We undertake a formal derivation of a linear poro-thermo-elastic system within the framework of quasi-static deformation. This work is based upon the well-known derivation of the quasi-static poroelastic equations (also known as the Biot consolidation model) by homogenization of the fluid-structure interaction at the microscale. We now include energy, which is coupled to the fluid-structure model by using linear thermoelasticity, with the full system transformed to a Lagrangian coordinate system. The resulting upscaled system is similar to the linear poroelastic equations, but with an added conservation of energy equation, fully coupled to the momentum and mass conservation equations. In the end, we obtain a system of equations on the macroscale accounting for the effects of mechanical deformation, heat transfer, and fluid flow within a fully saturated porous material, wherein the coefficients can be explicitly defined in terms of the microstructure of the material. For the heat transfer we consider two different scaling regimes, one where the Péclet number is small, and another where it is unity. We also establish the symmetry and positivity for the homogenized coefficients.     

一种新的振动叠加气动耦合加载技术

飞机机动飞行时,机体结构受到随机振动叠加气动的耦合载荷作用,有可能迅速产生破坏。为了考核在这种振动环境下飞机的结构强度及使用寿命能否达到设计要求,需要提供有效的地面试验验证手段和可靠的试验数据。本文研究了一种振动叠加气动的耦合载荷加载技术,通过液压球头传递振动载荷,同时通过气囊施加气动载荷,并设计进行了原理性验证试验。试验结果表明,这种耦合载荷加载技术可以避免过多改变试件自身的振动特性,同时可精确实现振动叠加气动的耦合载荷加载,真实模拟试验件的振动工作环境。此项技术可应用于现代战机的地面结构强度研究。     

Impact of Effective Stress and Matrix Deformation on the Coal Fracture Permeability

The permeability of coal is an important parameter in mine methane control and coal bed methane exploitation because it determines the practicability of methane extraction. We developed a new coal permeability model under tri-axial stress conditions. In our model, the coal matrix is compressible and Biot’s coefficient, which is considered to be 1 in existing models, varies between 0 and 1. Only a portion of the matrix deformation, which is represented by the effective coal matrix deformation factor $f_\mathrm{m}$ , contributes to fracture deformation. The factor $f_\mathrm{m}$ is a parameter of the coal structure and is a constant between 0 and 1 for a specific coal. Laboratory tests indicate that the Sulcis coal sample has an $f_\mathrm{m}$ value of 0.1794 for $\hbox {N}_{2}$ and $\hbox {CO}_{2}$ . The proposed permeability model was evaluated using published data for the Sulcis coal sample and is compared to three popular permeability models. The proposed model agrees well with the observed permeability changes and can predict the permeability of coal better than the other models. The sensitivity of the new model to changes in the physical, mechanical and adsorption deformation parameters of the coal was investigated. Biot’s coefficient and the bulk modulus mainly affect the effective stress term in the proposed model. The sorption deformation parameters and the factor $f_\mathrm{m}$ affect the coal matrix deformation term.     

Effect of Variations in the Interfacial Internal Energy on the Stability of a Two-Layer Poiseuille Flow

Calculations [1] showed that for fairly low-viscosity fluids variations of the internal energy of the interface due to local increments in its area can significantly affect the evolution of the temperature and velocity fields. In the present paper the possible effect of this theoretically predicted event on the linear and weakly nonlinear longwave instability of a plane interface between viscous fluids is considered in the case of an isothermal ground state. In the approximation considered, the effect is dispersive and leads to variation of the phase wave velocity and laminarization of the dynamics in the nonlinear stage of perturbation development.     

基于试验与有限元耦合技术的延性材料全程单轴本构关系获取方法

摘 要: 材料拉伸直至断裂的全程单轴本构关系对材料大变形和断裂机理研究具有重要意义。传统拉伸试验获取的材料真应力-真应变曲线在试样颈缩后不可测。借助可以精确测量三维变形的DIC(Digital image correlate) 技术和有限元分析技术(Finite element analysis),本文提出了基于漏斗试样拉伸试验获取材料全程单轴本构关系的新方法,即TF(Test and FEA)方法。该方法将TF方法获取的材料全程单轴应力应变关系曲线作为有限元软件中的材料本构关系对漏斗试样拉伸变形过程进行模拟,其模拟载荷-位移曲线、漏斗根部直径-位移曲线和漏斗变形轮廓线等均与试验结果吻合良好,试样表面模拟应变也与DIC测试结果吻合, 根据不同半径漏斗试样模拟获得的全程真应力-真应变曲线保持良好一致性。最后,还对试样颈缩断面的力学行为进行了讨论,并给出了304不锈钢、汽轮机叶片材料2Cr12Ni4Mo3VNBN和 1Gr12Ni3Mo2VN、汽轮机转子材料30Cr2Ni4MoV的全程单轴本构关系模型参数、破断应力和破断应变。     

A Structured Approach to the Derivation of Effective Properties for Combined Water and Gas Flow in the EDZ

The generation, accumulation, and release of corrosion gases is an important issue in the assessment of long-term repository performance. For repository concepts in clay-rich rock formations such as the Opalinus Clay of Northern Switzerland the transport path through the Excavation Damage Zone (EDZ) around the emplacement tunnels is of particular interest because the gas transport capacity of the host rock is limited and therefore a significant fraction of the produced gas could be released along the EDZ. This article describes the development of a structured approach to abstract complex geoscientific models of two-phase flow through the EDZ to simplified models suitable for use within a Probabilistic Safety Assessment (PSA). The approach utilizes three different models: a discrete fracture network (DFN) model of the EDZ, an equivalent heterogeneous continuum porous medium (CPM) model and a simplified CPM model suitable for use within PSA. Equivalent properties of the elements of the heterogeneous CPM models are upscaled from DFN realizations. Results from gas injection simulations with the heterogeneous CPM models are then used to derive appropriate parameters for the simplified CPM model. The modeling presented in this article represents the first step in the development of a structured methodology for treatment of gas, solute, and water flow through the EDZ. The emphasis is on methodology development, and both input data and structural models used in this study are of a generic nature and would have to be adapted to the actual conditions at a real repository site.     

用显微云纹干涉法研究SiC/Ti-15-3界面热残余应力场

SiC/Ti-15-3复合材料基体与增强体之间的热膨胀系数存在显著差异。在复合材料制造过程中经高温冷却后,在基体与增强体的界面会产生热残余应力场。此残余应力场对复合材料的力学性能会产生重要的影响。本文运用纤维推出法推出部分SiC纤维后,采用显微云纹干涉法在细观尺度研究了上述界面处的热残余应力,得到了分辨率较高的云纹图,并由此计算出了孔边处的残余应力。用有限元软件对界面热残余应力进行了数值模拟分析。实验结果表明,显微云纹干涉法可以用来测量直径为0.1 mm左右的纤维界面附近的残余应力场,在此尺度下,使用显微云纹干涉法比用电子束云纹法更方便。     

基于应力波传播机理的混凝土无损检测研究综述

混凝土结构在基础设施中应用广泛,但环境与荷载导致材料和结构的老化损伤问题,势必影响材料性能及耐久性和结构完整性及安全性.构建有效的混凝土材料性能评估和结构损伤识别体系是当前研究热点.现有研究因对应力波传播机理不深入理解、损伤定位定量模型理想化、损伤形式简化等问题仍存在局限性.因此,开发普适全面、稳定可靠的无损检测系统,对在建或既有混凝土结构服役状况进行长期、实时跟踪,具有重要学术意义和工程应用价值.本文结合混凝土无损检测领域的国内外研究现状及进展,从智能压电材料振动机理研究、混凝土无损检测方法发展、基于应力波的无损检测研究进展这三个逻辑层面,即按照研究手段到研究方法再到具体研究方案的顺序,循序渐进地对混凝土材料性能评估和结构损伤识别的研究进行了成果总结和方法提炼;基于此进一步概述了该领域所存在的瓶颈问题、研究重难点,最后提出了针对这些局限性的混凝土无损检测研究展望.     

An Energy Approach to the Calculation of Forces Acting on Solid Bodies in Ferrofluids

Journal of Applied Mechanics and Technical Physics - The main advantages of the energy approach to solving the problem of determining magnetic forces acting on solid bodies immersed into magnetized...     

基于动柔度法的门杆耦合

本文基于动柔度法法计算了闸门与启闭杆耦合的结构动态特性,比较了门杆开启的两种运行方式,初步探讨了抗振中门杆的相互关系     

Investigation of Transport- and Sorption-Related Factors on the Removal of Hydrophobic Organic Compounds in Heterogeneous Soils Using a Hierarchical Modeling Approach

Hydrophobic organic compounds (HOCs) represent a class of generally highly persistent contaminants in groundwater. Factors influencing the transport of HOCs are evaluated through a hierarchical modeling approach, which incorporates particle scale sorption/diffusion with pore scale flow and transport models. The relative contributions of transport- and sorption-related factors on HOCs transport are first elucidated in a simplified single particle system. The comparative roles of different soil organic matter contents and compositions on the fate and transport of HOCs are further investigated by simulation of phenanthrene transport in porous media. This effort represents a proof-of-concept demonstration of bridging comprehensive representations of fluid-flow with mechanistic sorption/desorption processes.     

芯片封装焊球连接疲劳寿命预测分析--能量法和有效应变法之比较

研究了目前常用的两种芯片封装焊球连接的寿命预测方法一能量法和有效应变法。对焊球连接的材料本构关系进行了对比分析，并利用FORTRAN语言编制了相应的材料本构模型子程序，将其与有限元仿真工具ANSYS耦合，实现了将焊球连接的材料本构模型用户子程序导入到ANSYS的材料库。在此基础上模拟了三维芯片叠层球栅阵列尺寸封装的焊球结构，在热循环条件下(-40～ 125℃的工作状态，并分别利用能量法和有效应变法对焊球连接的寿命预测进行了比较分析，最后对两种方法作出了评价。     

A Lattice Gas Automaton Simulation of the Nonlinear Diffusion Equation: A Model for Moisture Flow in Unsaturated Porous Media

We investigate a two-dimensional lattice gas automaton (LGA) for simulating the nonlinear diffusion equation in a random heterogeneous structure. The utilility of the LGA for computation of nonlinear diffusion arises from the fact that, the diffusion coefficient in the LGA depends on the local density of fluid particles which statistically determines the collision rate and thus, the mean free path of the particles at the microscopic scale. The LGA may therefore be used as a physical analogue to simulate moisture flow in unsaturated porous media. The capability of the LGA to account for unsaturated flow is tested through a set of numerical experiments simulating one-dimensional infiltration in a simplified semi-infinite homogenous isotropic porous material. Different mechanisms of interactions are used between the fluid and the solid phase to simulate various fluid–solid interfaces. The heterogeneous medium, initially at low density is submitted to a steep density gradient by continuously injecting fluid particles at high concentration and zero velocity along one face of the model. The propagation of the infiltration front is visualized at different time steps through concentration profiles parallel to the applied concentration gradient and the infiltration rate is measured continuously until steady-state flow is reached. The numerical results show close agreement with the classical theory of flow in unsaturated porous media. The cumulative absorption exhibits the expected t ^1/2 dependence. The evolution of the effective diffusion coefficient with the particle concentration is estimated from the measured density profiles for the various porous materials. Depending on the applied fluid–solid interactions, the macroscopic effective diffusivity may vary by more than two orders of magnitude with density.     

A Meshless Solution Technique for the Solution of 3D Unsaturated Zone Problems,Based on Local Hermitian Interpolation with Radial Basis Functions

Recent developments in meshless numerical methods have led to algorithms that can be used to solve arbitrarily large problems without the support of a connected mesh, and without the computational cost and numerical ill-conditioning issues usually associated with such solution techniques. This work applies the Local Hermitian Interpolation (LHI) method, based on local interpolation with Radial Basis Functions (RBFs), to the solution of 3D unsaturated porous media problems. The proposed implementation is capable of handling real soil properties, provided either as an analytical function or as a series of pointwise measurements. The technique is implemented with implicit and explicit timestepping, and is validated against two transient Richards’ equation models, of which one has a known analytical solution. In addition, a real-world infiltration problem based on a saturated–unsaturated formulation is modelled, using a realistic variation of soil properties with water-pressure.     

A Surrogate Modelling Approach Based on Nonlinear Dimension Reduction for Uncertainty Quantification in Groundwater Flow Models

Transport in Porous Media - In this paper, we develop a surrogate modelling approach for capturing the output field (e.g. the pressure head) from groundwater flow models involving a stochastic...