层状岩体地下洞室的Cosserat理论有限元分析

采用一般有限元对互层岩体进行数值分析研究时,要求的单元数量多、建模工作量大;并且难以反映层状岩体的弯曲变形特性。针对这种岩体Cosserat介质模型是一种很有用的有限元等效模型。首先对基于平面应变问题的Cosserat介质理论及扩展模型简略介绍,然后导出了模型的Mohr-Coulomb塑性屈服条件。再利用Matlab平台编制有限元程序,并对地下洞室工程进行数值模拟。将所得结果与传统连续介质法的结果进行对比。结果表明,基于Matlab的Cosserat有限元程序的有效性及解决互层岩体这类问题的适用性与优越性。     

基于Cosserat连续体的颗粒破碎影响研究

颗粒破碎对颗粒材料宏观力学行为有重要影响。 结合Hardin的破碎经验公式,将表征破碎程度的破碎参量与Cosserat连续体的内部长度参数相关联,形成一个基于Cosserat连续体且能考虑颗粒破碎的弹塑性模型。数值算例主要考察了颗粒破碎对颗粒材料承载能力、塑性应变及局部化行为的影响,数值结果表明,颗粒破碎主要发生在剪切带内,颗粒破碎使得剪切带明显变窄且剪切带内外等效塑性应变梯度明显增大。     

基于Cosserat理论的重力坝深层抗滑稳定分析

重力坝深层滑动主要表现为沿缓倾角的软弱结构面形成滑移通道,滑移通道内应变积聚且应变梯度急剧不连续,是典型的应变局部化现象,采用经典连续介质理论进行数值模拟时存在病态的有限元网格依赖性。引入Cosserat连续体理论作为正则化机制,提出了基于Cosserat理论的Mohr-Coulomb弹塑性模型,考虑非关联的流动法则,在经典塑性理论框架下采用向后Euler隐式积分算法进行应力更新。采用ABAQUS的自定义单元接口（UEL）进行二次开发,进行了平面应变条件下单轴受压的数值验证。数值模拟结果表明,该模型能保证应变局部化问题的正定性。基于Cosserat理论的重力坝深层抗滑稳定分析结果表明,采用超载法进行重力坝渐进破坏过程模拟时,基于经典连续体理论的模拟结果有较大的网格依赖性,而且结果偏于安全,而采用Cosserat连续体理论的结果对网格密度不敏感。     

Structural softening,mesh dependence,and regularisation in non-associated plastic flow

A severe dependence of numerical simulations on the mesh density is usually attributed to the presence of strain softening in the constitutive relation. However, other material instabilities, like non-associated plastic flow, can also cause mesh sensitivity. Indeed, loss of ellipticity in quasi-static analyses is the fundamental cause of the observed mesh dependence. It has been known since long that non-associated plastic flow can cause loss of ellipticity, but the consequence for mesh sensitivity, and subsequently, for the difficulty of the equilibrium-finding iterative procedure to converge have remained largely unnoticed. We first demonstrate at the hand of a biaxial test structural softening and a marked mesh dependence for an ideally plastic material equipped with a non-associated flow rule. The phenomena are then analysed in depth using an infinitely long shear layer. Finally, it is shown that the mesh effect disappears when the standard continuum model is replaced by a Cosserat continuum, a well-known regularisation method for strain-softening constitutive relations.     

The role of non‐coaxiality in the simulation of strain localization based on classical and Cosserat continua

It is normally accepted that materials inside the shear band undergo severe rotation of the principal stress direction, which causes non‐coaxiality between the principal stress and principal plastic strain rate. However, classical plasticity flow theory implicitly assumes that the principal stress and the principal plastic strain rate are coaxial; thus, it may not correctly predict the onset of the shear band. In addition, classical continuum does not contain any internal length scales; as a result, it cannot provide a reasonable shear band thickness. In this study, the original vertex non‐coaxial plastic model based on the classical continuum is extended to the Cosserat continuum. The corresponding codes are implemented via the interface of the user defined element subroutine in ABAQUS. Through a simple shear test, the effectiveness of the user's codes is verified. Through a uniaxial compression test, the influence of non‐coaxiality on the onset, the orientation, and the thickness of the shear band is investigated. Results show that the onset of the shear localization is delayed, and the thickness of the shear band is widened when the non‐coaxial degree increases, while the orientation of the shear band is little affected by the non‐coaxial degree. In addition, it is found that the non‐coaxiality can weaken the micro‐polar effect to some extent; nonetheless, the Cosserat non‐coaxial model still has its advantage over the classical non‐coaxial model in capturing the pre‐bifurcation as well as the post‐bifurcation behaviors of strain localization. Copyright © 2016 John Wiley & Sons, Ltd.     

Three-dimensional Cosserat homogenization of masonry structures: elasticity

Masonry is a two-phase composite material formed by regularly distributed bricks and mortar. The homogenization procedure followed here extends the 2D approach of Sulem and Mühlhaus (Mech Cohesive Frict Mater 2:31–46, 1997) and leads to an anisotropic 3D Cosserat continuum. The enriched kinematics of the Cosserat continuum allows us to model microelement systems undergoing in-plane and out-of-plane rotations. The domain of validity of the derived Cosserat continuum is discussed by comparing the dispersion function of the discrete system of blocks with the continuous one and is found to be in good agreement.     

土方开挖粘塑性模糊随机损伤机理研究

以基坑工程为例分析了开挖损伤演变的模糊随机性并建立了广义非确定性空间O：Б（s,f）。提出了初始损伤有效张量的概念模型,在“损伤源汇”概念基础上提出了模糊衰减模型,构造了粘塑性模糊随机损伤增量方程并实现了基坑开挖过程的模糊随机损伤模拟。在线性算子基础上提出了模糊随机损伤矢量极限值{Ωu},进而建立了以损伤有效张量为基础的粘塑性模糊随机损伤本构模型及粘塑性非线性模糊随机数值方法。在粘塑性模糊随机损伤有限元基础上建立了粘塑性模糊随机损伤变化率方程,实现了对基坑开挖过程中模糊随机损伤演变发展的全面模拟,完成了模糊随机卸荷损伤模型的构建。     

地基渐进破坏及极限承载力的Cosserat连续体有限元分析

利用Cosserat连续体理论和所发展的有限元数值方法,模拟了地基由应变软化引起的以应变局部化为特征的渐进破坏过程,并从等价塑性应变的发展变化,阐述了渐进破坏过程对所能发挥的极限承载能力的影响。结果表明,Cosserat连续体模型能有效地模拟由应变软化引起以应变局部化为特征的渐进破坏现象,对地基等土工结构物有必要进行渐进破坏分析。同时指出,在求解软化型土体地基的极限承载力时,如果仍按传统的极限平衡或极限分析理论进行分析,可能得出偏于危险的结果。     

A continuum model of layered rock masses with non-associative joint plasticity

Layered rock masses can be modelled either as standard, orthotropic continua if the layer bending can be neglected or as Cosserat continua if the influence of layer bending is essential. This paper presents a finite element smeared joint model based on the Cosserat theory. The layers are assumed to be elastic with equal thickness and equal mechanical properties. All the cosserat parameters are expressed through the elastic properties of layers, layer thickness and joint stiffness. Plastic-slip as well as tensile-opening of layer interface (joint) are accounted for in a manner similar to the conventional non-associative plasticity theory. As an application, the behaviour of an excavation in a layered rock mass is examined. The displacement and stress fields given by smeared joint models based on the Cosserat continuum and the conventional anisotropic continuum approaches are compared with those obtained from the discrete joint model. The conventional anisotropic continuum model is found to break-down completely when the effective shear modulus in the direction parallel to layering is low in comparison to the shear modulus of the intact layer, whereas the Cosserat model is found to be capable of accurately reproducing complex load–deflection patterns irrespective of the differences in shear moduli. © 1998 John Wiley & Sons, Ltd.     

An Orthotropic Cosserat Elasto-Plastic Model for Layered Rocks

Summary Modelling the behaviour of rock masses consisting of a large number of layers is often necessary in mining applications (e.g. coal mining). Such a modelling can be carried out in a discontinuum manner by explicit introduction of joints. When the number of rock layers is large, it is advantageous to devise a continuum-based model in which case the joints are considered to be virtually smeared across the mass. In this study, a fully elasto-plastic equivalent continuum model suitable for describing the behaviour of such layered rock masses is considered. The model is based on the Cosserat continuum theory and incorporates the moment stresses in its formulation. In contrast to the earlier Cosserat models, the possibility of rock layer plasticity is considered. The accuracy of the developed Cosserat model is verified against analytical and experimental results. Received October 15, 2000; accepted July 30, 2001 Published online August 2, 2002     

A micromechanics-based elasto-plastic model for granular media combined with Cosserat continuum theory

Acta Geotechnica - This paper is devoted to the micromechanical model of granular materials based on the Cosserat continuum theory. The generalised stress–strain relationships of a...     

Experimental and numerical study of sand–steel interfaces

Experimental and numerical studies on and sand–steel interfaces are presented. Emphasis is laid on the effect of boundary conditions of the whole system and of localized deformation. The experiments with different roughness of steel surface, sand density, normal stress and grain size are carried out in a plane strain apparatus, a parallely guided direct shear apparatus and in a planar silo model with a movable bottom and parallel steel walls. During the test in the plane strain apparatus the localized zone is observed with the help of X-rays. The results indicate a significant effect of wall roughness and boundary conditions of the whole system on the wall friction angle and the thickness of the localized zone along the steel surface. An elastoplastic constitutive model established within the framework of a Cosserat continuum, capable of describing isotropic hardening, softening and dilatancy, is implemented in a finite element code. The model differs from the conventional theory of plasticity due to the presence of Cosserat rotation and couple stress using the mean grain diameter as the characteristic length. Finite element simulations of simple shear tests are presented. The additional boundary condition along the steel plate, characteristic of the Cosserat continuum, allows for modelling the different roughness of the steel plate with consideration of grain rotations. A comparison between the numerical calculations and the experimental results shows acceptable agreement.     

Borehole failure analysis in a sandstone under anisotropic stresses

Borehole failure under anisotropic stresses in a sandstone is analyze numerically for various borehole sizes using a nonlinear elastic–plastic constitutive model for a Cosserat continuum. Borehole failure is identified as macroscopic failure of the borehole through the development of shear bands and breakouts. The results compare well both qualitatively and quantitatively with experimental results from polyaxial tests on Red Wildmoor sandstone. They show that the hole size effect of the borehole failure strength is independent of the far‐field stress anisotropy and follows a ? power law of the hole size. A similar scale effect equation with a ? power law is proposed for the scale effect of the maximum plastic shear strain at failure. This equation can be useful for better predicting hole‐size‐dependent failure with standard codes based on classical continua. The effect of stress anisotropy on the borehole failure stress is found to be independent of the hole size. The failure stress decreases linearly to 40% as the stress anisotropy increases. However, the maximum plastic shear strain at failure is stress anisotropy independent and therefore the critical plastic shear strain for failure is only hole‐size dependent. Copyright © 2009 John Wiley & Sons, Ltd.     

Effects of periodic fluctuations of micro‐polar boundary conditions on shear localizations in granular soil–structure interaction

In this work, the interface behavior between an infinite extended narrow granular layer and a rough surface of rigid body is investigated numerically, using finite element method in the updated Lagrangian (UL) frame. In this regard, the elasto‐plastic micro‐polar (Cosserat) continuum approach is employed to remove the limitations caused by strain‐softening of materials in the classical continuum. The mechanical properties of cohesionless granular soil are described with Lade's model enhanced by polar terms, including Cosserat rotations, curvatures, and couple stresses. Furthermore, the mean grain diameter as the internal length is incorporated into the constitutive relations accordingly. Here, the evolution and location of shear band, within the granular layer in contact with the rigid body, are mainly focused. In this regard, particular attention is paid to the effects of homogeneous distribution and periodic fluctuation of micro‐polar boundary conditions, prescribed along the interface. Correspondingly, the effects of pressure level, mean grain diameter, and stratified soil are also considered. The finite element results demonstrate that the location and evolution of shear band in the granular soil layer are strongly affected by the non‐uniform micro‐polar boundary conditions, prescribed along the interface. It is found that the shear band is located closer to the boundary with less restriction of grain rotations. Furthermore, the predicted thickness of shear band is larger for higher rotation resistance of soil grains along the interface, larger mean grain diameter, and higher vertical pressure. Regarding the stratified soil, comprising a thin layer with slightly different initial void ratio, the shear band moves towards the layer with initially higher void ratio. Copyright © 2011 John Wiley & Sons, Ltd.     

A numerical study of flexural buckling of foliated rock slopes

The occurrence of foliated rock masses is common in mining environment. Methods employing continuum approximation in describing the deformation of such rock masses possess a clear advantage over methods where each rock layer and each inter‐layer interface (joint) is explicitly modelled. In devising such a continuum model it is imperative that moment (couple) stresses and internal rotations associated with the bending of the rock layers be properly incorporated in the model formulation. Such an approach will lead to a Cosserat‐type theory. In the present model, the behaviour of the intact rock layer is assumed to be linearly elastic and the joints are assumed to be elastic–perfectly plastic. Condition of slip at the interfaces are determined by a Mohr–Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformations. The model is incorporated into the finite element program AFENA and validated against an analytical solution of elementary buckling problems of a layered medium under gravity loading. A design chart suitable for assessing the stability of slopes in foliated rock masses against flexural buckling failure has been developed. The design chart is easy to use and provides a quick estimate of critical loading factors for slopes in foliated rock masses. It is shown that the model based on Euler's buckling theory as proposed by Cavers (Rock Mechanics and Rock Engineering 1981; 14 :87–104) substantially overestimates the critical heights for a vertical slope and underestimates the same for sub‐vertical slopes. Copyright © 2001 John Wiley & Sons, Ltd.     

随机覆盖下堤坝填筑工程非线性可靠度理论研究

基于Mohr-Coulomb破坏准则下材料的非线性特征,结合粘塑性应力空间内破坏准则被有限超越期间的稳定时间步长,对随机数学覆盖下粘塑性数值算法的逻辑实现过程进行推导,在直接偏微分理论基础上建立了三维及平面应变条件下粘塑性非线性随机有限元的本构关系式,进而提出了基于全量理论的粘塑性非线性随机有限元列式,并以堤防填筑工程为例,分析研究了土质堤坝分阶段逐步填筑过程中的随机演化机理及堤坝结构的可靠度安全性,实现了堤防填筑工程的全程随机模拟。     

颗粒材料平均场理论的多尺度方法：理论方面

对基于平均场理论的颗粒材料多尺度方法实施过程中的基本理论问题进行了探讨。公式推导表明,考虑微观颗粒间滚动矩相互作用时宏观需要采用Cosserat类连续体模型。基于平均场理论,给出了离散颗粒表征元等效连续介质应力、偶应力表达式。基于Hill-Mandel宏观均质化条件,给出了离散颗粒微结构波动场的边界条件,并且讨论了内部长度尺度参数的选择问题。该工作是颗粒材料多尺度计算的理论部分研究。     

Investigation into subsidence hazards due to groundwater pumping from Aquifer II in Changzhou,China

This paper presents an investigation into increased deformation of Aquifer II caused by groundwater pumping from the aquifer in Changzhou, China. As groundwater levels of aquifers have been decreasing in recent decades due to uncontrolled water pumping, land subsidence is becoming a serious geohazard in Changzhou. Based on recently reported field data, the compression of aquitards has not increased compared to that of aquifers with the same scale of layer thickness. The Cosserat continuum model was adopted to analyse the observed phenomenon in this study. A classic Cauchy continuum model is also used for comparison. The comparison between these two models indicates that the proposed approach can interpret the increased deformation well, and the classic Cauchy continuum model underestimates the aquifer deformation as it does not consider shear displacement and macro-rotation. A discussion on the relationship between the groundwater level in the aquifer and subsidence is then undertaken. The results show that the severity of the annual subsidence is correlated with the variation in groundwater level in Aquifer II. To mitigate the subsidence hazards, countermeasures should be adopted to avoid the shear stress in aquifers which results from the high hydraulic gradient, by the appropriate allocation of pumping wells and by restricting groundwater withdrawal volume from each pumping operation.     

Buckling of layered elastic media: A cosserat-continuum approach and its validation

In this paper the stability of layered, anisotropic, hypoelastic media under initial stress is investigated. The bifurcation problem is formulated and solved numerically by use of a semi-analytical transfer matrix method. An alternative analytical approach in dealing with inhomogeneous media is developed by representing a periodically layered medium as a homogeneous Cosserat continuum. The Cosserat-continuum approach is validated against the numerical transfer matrix solution.     

具有弯曲效应的层状结构岩体变形的Cosserat介质分析方法

在反倾向层状岩体边坡、有底鼓现象的巷道以及隧洞工程中，岩体常出现弯曲变形及弯曲破坏现象。常规的等效连续介质理论忽略了梯度应力的影响，因而不能很好解决上述工程问题．Ｃｏｓｓｅｒａｔ介质理论以具有一定尺度的微元体为研究对象，引进了偶应力及弯曲曲率概念，从而考虑了弯曲效应对介质变形特性的影响。本文首先介绍Ｃｏｓｓｅｒａｔ介质理论的基本原理，然后建立有限元计算模式，最后通过算例，说明这种模式对计算具有弯曲效应的展状岩体变形问题是有效的。