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1.
In this paper, a coupled constitutive model is proposed for anisotropic damage and permeability variation in brittle rocks under deviatoric compressive stresses. The formulation of the model is based on experimental evidences and main physical mechanisms involved in the scale of microcracks are taken into account. The proposed model is expressed in the macroscopic framework and can be easily implemented for engineering application. The macroscopic free enthalpy of cracked solid is first determined by approximating crack distribution by a second‐order damage tensor. The effective elastic properties of damaged material are then derived from the free enthalpy function. The damage evolution is related to the crack growth in multiple orientations. A pragmatic approach inspired from fracture mechanics is used for the formulation of the crack propagation criterion. Compressive stress induced crack opening is taken into account and leads to macroscopic volumetric dilatancy and permeability variation. The overall permeability tensor of cracked material is determined using a micro–macro averaging procedure. Darcy's law is used for fluid flow at the macroscopic scale whereas laminar flow is assumed at the microcrack scale. Hydraulic connectivity of cracks increases with crack growth. The proposed model is applied to the Lac du Bonnet granite. Generally, good agreement is observed between numerical simulations and experimental data. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
2.
Practical expressions are given for the nine components of the block-scale permeability tensor of a thin block. These expressions are derived from the local-scale continuity equation and Darcy's law in an anisotropic layered porous medium. The flow problem is separated in a bottom-flux problem and a top-flux problem, both of which can be solved in essentially the same way. The bottom-flux problem has been worked out in detail, and has been separated in two parts: a vertical potential difference and a horizontal potential difference part. Each is solved with a different approach specially designed for it. Depth-averaged expressions are obtained first, after which block-scale expressions are obtained by assuming a constant depth-averaged flux. In the zeroth order, this results in the well-known Dupuit approximation in geohydrology, and the vertical equilibrium (VE) approximation in petroleum reservoir engineering. The novelty of the theory presented here stems from the application of a perturbation technique to obtain first-order corrections to these well-known results. The local-scale laws are applied in the coordinate system coinciding with the principal axes of the local-scale permeability tensor. Only in this coordinate system the local-scale permeability tensor has zero off-diagonal components. However, since the porous medium is imperfectly layered, the first-order corrections show that the off-diagonal components of the block-scale permeability tensor are not zero. Furthermore, the block-scale permeability tensor is generally nonsymmetric, which implies that a coordinate system in which the off-diagonal terms disappear does not exist. 相似文献
3.
Fabric and its evolution need to be fully considered for effective modeling of the anisotropic behavior of cohesionless granular sand. In this study, a three‐dimensional anisotropic model for granular material is proposed based on the anisotropic critical state theory recently proposed by Li & Dafalias [2012], in which the role of fabric evolution is highlighted. An explicit expression for the yield function is proposed in terms of the invariants and joint invariants of the normalized deviatoric stress ratio tensor and the deviatoric fabric tensor. A void‐based fabric tensor that characterizes the average void size and its orientation of a granular assembly is employed in the model. Upon plastic loading, the material fabric is assumed to evolve continuously with its principal direction tending steadily towards the loading direction. A fabric evolution law is proposed to describe this behavior. With these considerations, a non‐coaxial flow rule is naturally obtained. The model is shown to be capable of characterizing the complex anisotropic behavior of granular materials under monotonic loading conditions and meanwhile retains a relatively simple formulation for numerical implementation. The model predictions of typical behavior of both Toyoura sand and Fraser River sand compare well with experimental data. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
4.
为了研究土体的细观渗流特性,假设土体是完全饱和且在渗流过程中水分的流动始终处于层流状态。考虑宏观统计参数（孔隙率、渗透率及有效黏滞系数等）的影响,基于表征体元（REV）尺度的格子博尔兹曼（Boltzmann）方法,建立了压力作用下土体细观渗流的数值模型。采用D2Q9模型考虑水分流动的离散速度分布,宏观边界条件为左右侧面为不透水边界 ,上下边界设置不同的密度来控制压力边界,在微观边界条件上采用非平衡态外推格式。编制相应的计算程序,将计算区域内的多孔介质材料设置成流体（孔隙率 1.0,渗透率 ）,验证了经典的Poiseuille流。此外,结合算例分别讨论了土体在压力作用下孔隙率、渗透率及渗透压力等影响因素与渗流速度的相互关系,研究表明该数值方法与Darcy定律得到的计算结果较为吻合。因此,基于REV尺度的格子Boltzmann方法可以有效地模拟土体的渗流机制,为进一步研究土体渗流特性提供了一种新的研究手段。 相似文献
5.
格子Boltzmann方法地震波场模拟 总被引：3，自引：0，他引：3
格子Ｂｏｌｔｚｍａｎｎ方法是细胞自动机在某些学科中的具体化和应用。它根据微观运动过程的某些基本特征建立简化的、时间和空间完全离散的动力学模型，这种模型的平行行为符合宏观的微分方程。 相似文献
6.
Lower bound limit analysis of an anisotropic undrained strength criterion using second‐order cone programming 
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下载免费PDF全文 In this paper, the formulation of the lower bound limit analysis of an anisotropic undrained strength criterion using second‐order cone programming is described. The finite element concept was used to discretize the soil mass into 3‐noded triangular elements. The stress field was modeled using a linear interpolation within the elements while stress discontinuities were permitted to occur at the shared edges of adjacent elements. An elliptical yield criterion was adopted to model the anisotropic undrained strength of the clay. A statically admissible stress field was defined by enforcing the equilibrium equations within all triangular elements and along all shared edges of adjacent elements, stress boundary conditions, and no stress violation of the anisotropic strength envelope cast in the form of a conic quadratic constraint. The lower bound solution of the proposed formulation was solved by second‐order cone programming. The proposed formulation of the anisotropic undrained strength criterion was validated through comparison of the model's predictions with the known exact solutions of strip footings, and was applied to solve undrained stability of a shallow unlined square tunnel. Computational performance between the proposed approach of second‐order cone programming and linear programming was examined and discussed. 相似文献
7.
In order to simulate the soil response during principal stress rotation, anisotropic unified hardening (UH) model is developed within the framework of elastoplastic theory. Without introducing any additional mechanism to display the role of stress rotation specifically, this model achieves the simulation by considering the material anisotropy. The effect of inherent anisotropy is reflected using the anisotropic transformed stress method, but a new formula for the stress mapping is adopted to keep the mean stress unchanged. Analysis indicates that from the view of the transformed stress tensor, the anisotropic soil is subjected to loading during pure rotation of principal stress axes, so that plastic strains can be calculated. To represent the induced anisotropy, a fabric evolution law is proposed based on laboratory and numerical test results. At the critical state, the fabric tensor reaches a stable value determined by the stress state, while the critical state line is unique in the plane of void ratio versus mean stress. The anisotropic UH model has concise formulation and explicit elastoplastic flexibility matrix and can provide reasonable predictions for the deformation of anisotropic soils when principal stresses rotate. 相似文献
8.
A simple method called anisotropic transformed stress (ATS) method is proposed to develop failure criteria and constitutive models for anisotropic soils. In this method, stress components in different directions are modified differently in order to reflect the effect of anisotropy. It includes two steps of mapping of stress. First, a modified stress tensor is introduced, which is a symmetric multiplication of stress tensor and fabric tensor. In the modified stress space, anisotropic soils can be treated to be isotropic. Second, a TS tensor is derived from the modified stress tensor for the convenience of developing anisotropic constitutive models to account for the effect of intermediate principal stress. By replacing the ordinary stress tensor with the TS tensor directly, the unified hardening model is extended to model the anisotropic deformation of soils. Anisotropic Lade's criterion is adopted for shear yield and shear failure in the model. The form of the original model formulations remains unchanged, and the model parameters are independent of the loading direction. Good agreement between the experimental results and predictions of the anisotropic unified hardening model is observed. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
9.
Non-ideality in mineral solid solutions affects their elastic and thermodynamic properties, their thermobaric stability, and the equilibrium phase relations in multiphase assemblages. At a given composition and state of order, non-ideality in minerals is typically modelled via excesses in Gibbs free energy which are either constant or linear with respect to pressure and temperature. This approach has been extremely successful when modelling near-ideal solutions. However, when the lattice parameters of the solution endmembers differ significantly, extrapolations of thermodynamic properties to high pressures using these models may result in significant errors. In this paper, I investigate the effect of parameterising solution models in terms of the Helmholtz free energy, treating volume (or lattice parameters) rather than pressure as an independent variable. This approach has been previously applied to models of order–disorder, but the implications for the thermodynamics and elasticity of solid solutions have not been fully explored. Solid solution models based on the Helmholtz free energy are intuitive at a microscopic level, as they automatically include the energetic contribution from elastic deformation of the endmember lattices. A chemical contribution must also be included in such models, which arises from atomic exchange within the solution. Derivations are provided for the thermodynamic properties of n-endmember solutions. Examples of the use of the elastic model are presented for the alkali halides, pyroxene, garnet, and bridgmanite solid solutions. Elastic theory provides insights into the microscopic origins of non-ideality in a range of solutions, and can make accurate predictions of excess enthalpies, entropies, and volumes as a function of volume and temperature. In solutions where experimental data are sparse or contradictory, the Helmholtz free energy approach can be used to assess the magnitude of excess properties and their variation as a function of pressure and temperature. The formulation is expected to be useful for geochemical and geophysical studies of the Earth and other planetary bodies. 相似文献
10.
An alternative approach for quasi‐static large deformation analysis of saturated porous media using meshfree method 下载免费PDF全文
下载免费PDF全文 An alternative coupled large deformation formulation combined with a meshfree approach is proposed for flow–deformation analysis of saturated porous media. The formulation proposed is based on the Updated Lagrangian (UL) approach, except that the spatial derivatives are defined with respect to the configuration of the medium at the last time step rather than the configuration at the last iteration. In this way, the Cauchy stresses are calculated directly, rendering the second Piola–Kirchhoff stress tensor not necessary for the numerical solution of the equilibrium equations. Moreover, in contrast with the UL approach, the nodal shape function derivatives are calculated once in each time step and stored for use in subsequent iterations, which reduces the computational cost of the algorithm. Stress objectivity is satisfied using the Jaumann stress rate, and the spatial discretisation of the governing equations is achieved using the standard Galerkin method. The equations of equilibrium are satisfied directly, and the nonlinear parts of the system matrix are derived independent of the stresses of the medium resulting in a stable numerical algorithm. Temporal discretisation is effected based on a three‐point approximation technique that avoids spurious ripple effects and has second‐order accuracy. The radial point interpolation method is used to construct the shape functions. The application of the formulation and the significance of large deformation effects on the numerical results are demonstrated through several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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路基冻胀问题严重影响寒区高速铁路的安全服役,而成冰相变过程是解释冻胀机制的关键。基于介观尺度的格子Boltzmann方法,将修正的孔隙水冻结温度算法与焓法固液相变格子Boltzmann模型相结合,模拟了悬浮液滴冻结和冻土孔隙水成冰两个过程,分别揭示了液态水在自由状态和孔隙束缚状态下冰水相变的细观机制。计算结果表明：土体孔隙中冰晶由中心向外生长的过程与悬浮在空气中的液滴冻结过程截然不同,并且孔隙水越接近颗粒表面,其冻结温度越低。相同粒径颗粒按照不同排列方式得到的冻结特征曲线（soil freezing characteristic curves,简称SFCC）具有明显差异;不同粒径的SFCC随着颗粒增大残余水含量逐渐变少,形态更加陡峭。通过与文献试验结果对比,验证了格子Boltzmann方法的有效性,表明该方法能够为研究多孔介质水气迁移与相变过程提供介观尺度的新手段。 相似文献
13.
In this paper, the factor of safety for a prescribed slip surface will be determined from an equivalent lower bound method (extremum principle), which can satisfy all equilibrium conditions without an interslice force function. This approach will give an overall factor of safety close to that from the classical methods for normal problems, while the thrust line, the local factor of safety for individual slice/block and the progressive yielding phenomenon can be estimated, which will be useful for some special cases. The force and moment equilibrium of every slice will be satisfied, while the location of the thrust line will always be acceptable in the present formulation. To solve the difficult optimisation problem, an innovative coupled particle swarm/harmony search algorithm is proposed in this paper, and a practical engineering problem for which the factor of safety is close to 1.0 is used to illustrate the consideration of the residual strength in the limit equilibrium slope stability analysis. 相似文献
14.
A matrix relating stress and elastic strain tensors for anisotropic particulate materials has been derived. The magnitude of the matrix depends on the state of the material anisotropy. Anisotropy in granular materials depends on strain because normal and tangential particle contact forces, as well as the spatial distribution of the contacts, vary with stress and strain. However, the rotation tensor and the strain tensor cannot be independent; they must satisfy certain constraints to meet the requirement for macroscopic stress tensor symmetry. These conditions and constraints lead to the derivation of the matrix presented in this article. The principal directions of the stress tensor and strain tensor are generally not coincident, and the values of deformation parameters, Young's modulus and Poisson's ratio, are direction dependent; these two aspects are also discussed in this paper. Whereas this matrix can be used in static numerical analyses for elastic problems, we note that this relationship can also be used as a basis upon which to derive a fully incremental stress–strain relationship for anisotropic granular materials in the plastic state, where the anisotropy is evolving with strain. 相似文献
15.
The pure cross-anisotropy is understood as a special scaling of strain (or stress). The scaled tensor is used as an argument in the elastic stiffness (or compliance). Such anisotropy can be overlaid on the top of any elastic stiffness, in particular on one obtained from an elastic potential with its own stress-induced anisotropy. This superposition does not violate the Second Law. The method can be also applied to other functions like plastic potentials or yield surfaces, wherever some cross-anisotropy is desired. The pure cross-anisotropy is described by the sedimentation vector and at most two constants. Scaling with more than two purely anisotropic constants is shown impossible. The formulation was compared with experiments and alternative approaches. Static and dynamic calibration of the pure anisotropy is also discussed. Graphic representation of stiffness with the popular response envelopes requires some enhancement for anisotropy. Several examples are presented. All derivations and examples were accomplished using the algebra program Mathematica.
相似文献16.
本文介绍了细胞自动机模型，九点格子Ｂｏｌｔｚｍａｎｎ方法和正六边形格子Ｂｏｌｔｚｍａｎｎ方法，研究了一个基于九点格子方法的卡门涡街问题，得到了满意的结果。 相似文献
17.
Interaction between solid particles and fluid is of fundamental interest to scientists and engineers in many different applications—cardiopulmonary flows, aircraft and automobile aerodynamics, and wind loading on buildings to name a few. In geomechanics, particle shape significantly affects both particle-particle and particle-fluid interaction. Herein, we present a generalized method for modeling the interaction of arbitrarily shaped polyhedral particles and particle assemblages with fluid using a coupled discrete element method (DEM) and lattice Boltzmann method (LBM) formulation. The coupling between DEM and LBM is achieved through a new algorithm based on a volume-fraction approach to consider three-dimensional convex polyhedral particles moving through fluid. The algorithm establishes the interaction using linear programming and simplex integration and is validated against experimental data. This approach to modeling the interaction between complex polyhedral particles and fluid is shown to be accurate for directly simulating hydrodynamic forces on the particles. 相似文献
18.
岩土材料的强度往往表现出很强的各向异性,而已有的各向同性强度准则不能够描述这一特性。提出一个岩土材料的各向异性强度准则。为了描述材料的各向异性,引入了一个由应力张量和组构张量的联合不变量表达的各向异性参数。该参数可以描述加载方向和材料组构方向的夹角。强度准则是基于材料在子午面和偏平面上的破坏特性而建立的,这为描述广义的材料强度各向异性提供了方便。与原各向同性强度准则相比,各向异性强度准则只引入了两个新的模型参数,而且所有的模型参数都可以通过常规的室内试验结果确定。该准则的预测结果与砂土、黏土、天然黏土和岩石的试验结果比较表明,它能够很好地描述岩土材料强度的各向异性 相似文献
19.
Thermochronometry based on radiogenic noble gases is critically dependent upon accurate knowledge of the kinetics of diffusion. With few exceptions, complex natural crystals are represented by ideal geometries such as infinite sheets, infinite cylinders, or spheres, and diffusivity is assumed to be isotropic. However, the physical boundaries of crystals generally do not conform to ideal geometries and diffusion within some crystals is known to be anisotropic. Our failure to incorporate such complexities into diffusive models leads to inaccuracies in both thermal histories and diffusion parameters calculated from fractional release data. To address these shortcomings we developed a code based on the lattice Boltzmann (LB) method to model diffusion from complex 3D geometries having isotropic, temperature-independent anisotropic, and temperature-dependent anisotropic diffusivity. In this paper we outline the theoretical basis for the LB code and highlight several advantages of this model relative to more traditional finite difference approaches. The LB code, along with existing analytical solutions for diffusion from simple geometries, is used to investigate the affect of intrinsic crystallographic features (e.g., crystal topology and diffusion anisotropy) on calculated diffusion parameters and a novel method for approximating thermal histories from crystals with complex topologies and diffusive anisotropy is presented. 相似文献
20.
In this paper, we propose a micromechanical approach of the behavior of granular media, which takes into account the anisotropy by means of a fourth order fabric tensor. The proposed approach is implemented in an homogenization scheme based on Voigt and Reuss localization assumption. The fabric tensor-based approach is then combined with a new kinematic localization rule and yields a general homogenization scheme for anisotropic granular media. 相似文献