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1.
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. 相似文献
2.
An Orthotropic Cosserat Elasto-Plastic Model for Layered Rocks 总被引：3，自引：1，他引：3
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 相似文献
3.
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。 相似文献
4.
The role of non‐coaxiality in the simulation of strain localization based on classical and Cosserat continua 
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下载免费PDF全文 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. 相似文献
5.
反倾层状岩体斜坡弯曲-拉裂两种失稳破坏之判据探讨 总被引：11，自引：4，他引：7
对反倾层状岩体斜坡弯曲-拉裂的失稳破坏判据,已有研究分别基于两种力学模型进行推导,即竖直压杆弹性屈曲稳定和平直梁弯折破坏模型,但对层间错动阻力及挠度产生附加弯矩等因素未加以考虑,不尽合理。在反倾斜坡岩层受力分析基础上,建立考虑了板侧层间错动阻力的下端嵌固、上端自由的斜置等厚弹性悬臂板梁模型,统一地通过瑞利-里兹能量方法,推导了弹性屈曲临界条件和嵌固端弯折破坏临界条件。实例计算及讨论表明,弹性屈曲判据适用于陡立岩层;而中-陡反倾岩层应主要为弯折破坏,但层间的力学性质对弯折临界判据值具有较大影响。 相似文献
6.
Euripides Papamichos 《国际地质力学数值与分析法杂志》2010,34(6):581-603
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. 相似文献
7.
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. 相似文献
8.
考虑塑性应变率梯度的单轴压缩岩样轴向响应 总被引：9，自引：7，他引：2
基于剪切应变率梯度格式,采用解析方式研究了岩石材料在单轴压缩条件下的应变软化的结构响应。根据非局部连续介质模型,提出了一维二阶剪切应变率梯度格式。非局部剪切应变率与局部剪切应变率及其二阶梯度有关。将经典塑性理论中的局部剪切应变率替换为非局部剪切应变率,可以直接得到局部剪切应变率的封闭解析解,而不必通过将局部剪切应变对时间求导获得。通过对局部剪切应变率积分,得到了沿剪切带方向的相对剪切速度。试件峰值强度后的端部速度由弹性及塑性两部分构成。前一部分由虎克定律描述;后一部分与相对剪切速度有关。对弹性及塑性两部分速度求和,得到了单轴压缩岩样剪切破坏问题轴向响应的解析式。研究表明：试样高度越大、内部长度越小、剪切软化模量越大及泊松比越小,则岩样的轴向响应倾向于脆性。根据岩样与矿柱的相似性,岩样响应倾向于脆性,意味着矿柱将失去稳定性,发生矿柱岩爆。目前的基于剪切应变率梯度格式的主要优点是简洁。 相似文献
9.
The paper deals with numerical investigations of the behaviour of granular bodies during shearing. Shearing of a narrow layer of sand between two very rough boundaries under constant vertical pressure is numerically modelled with a finite element method using a hypoplastic constitutive relation within a polar (Cosserat) continuum. The constitutive relation was obtained through an extension of a non‐polar one by polar quantities, viz. rotations, curvatures, couple stresses using the mean grain diameter as a characteristic length. This relation can reproduce the essential features of granular bodies during shear localization. The material constants can be easily determined from element test results and can be estimated from granulometric properties. The attention is laid on the influence of the initial void ratio, pressure level, mean grain diameter and grain roughness on the thickness of shear zones. The results of shearing are also compared to solutions without the polar extensions. The FE‐calculations demonstrate that polar effects manifested by the appearance of grain rotations and couple stresses are significant in the shear zone, and its thickness is sensitive to the initial void ratio, mean grain diameter and layer height. The effect of the pressure level is rather low within the considered range. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
10.
This paper concerns the buckling analysis of three-dimensional (3D) layered continua using the Cosserat approach. The finite element method (FEM) is used to implement the adopted Cosserat formulation. As a result, the interfaces between the layers need not be explicitly modelled. Instead, the internal characteristic length, i.e., the layer thickness and also the interaction conditions between the layers are incorporated into the governing equations of the solution. This paper introduces a new 3D geometric stiffness matrix based on the principle of virtual work. The proposed geometric stiffness matrix is applied to the linear buckling analysis of a number of benchmark problems with various geometries, boundary conditions, and interaction conditions between the layers. In all cases, the FEM Cosserat solution exhibits a high level of consistency with the analytical solution. 相似文献
11.
层状盐岩体的三维Cosserat介质扩展本构模 总被引：20，自引：3，他引：17
考虑到深部地下岩土工程一般是较复杂的三维问题,在层状盐岩体二维Cosserat介质扩展本构模型基础上,针对不同岩层交替而成的互层盐岩体,建立了宏观平均意义下考虑细观弯曲效应的三维Cosserat介质扩展本构模型,并给出了模型的初步试验验证。该模型既能分析硬（软）夹层对层状盐岩体刚度的强化（弱化）作用,又能考虑由于夹层的存在而导致的层状盐岩构造体宏观意义下力学特性的各向异性,为层状盐岩体及其他层状介质变形和破损分析提供了一种新的思路和方法。该模型可直接推广到非线性问题。结合数值分析软件可进行层状介质体内复杂洞室稳定性分析。 相似文献
12.
常规频散曲线反演过程中需要不停地改变分层数、层厚度和层速度等参数,实现过程相对繁琐,而采用细化分层法对反演参数进行简化则避免了上述缺点。具体思路为：根据目的层探测深度（如20m）将地下介质分为若干个（20个）厚度为1m的薄层和1个均匀半空间层（共21层）,这样在反演中分层数和层厚度均为已知参量,反演过程只需修改速度参数即可,避免了改变分层数和层厚度等参数,显著简化了反演计算过程。正演计算和反演结果均表明：细化分层与实际分层计算出的频散曲线是等效的,细化分层反演结果的总体效果与真实模型非常接近,这说明细化分层方法用于频散曲线反演是切实可行且有效的;将地下介质划分为1m厚的薄层,反演后每层均可得到1个横波速度,能满足反演分辨率的要求;由于实际地下介质的速度是随深度渐变的,细化分层后比按频散曲线拐点分层（每分层的厚度可能是几米或几十米,同一分层内介质的横波速度相等）更接近实际情况。 相似文献
13.
Deformation of host rocks during growth of a laccolithic intrusion is analyzed using the theory of bending a stack of thin elastic plates. The theoretical model suggests that magma spreading laterally in the form of a sill will eventually gain sufficient leverage on the overlying strata to deflect them upward and form a laccolith. The amount of bending increases as the fourth power of the distance the magma spreads, whereas the overburden resists bending as the third power of its effective thickness. Effective thickness is the thickness of a single layer which has the same resistance to bending as a multilayer of similar length and elastic modulus. The effective thickness of overburden in the Henry Mountains is estimated as between
and
of the actual thickness. The form of bending is similar for Newtonian, pseudoplastic, and Bingham magmas. The magnitude of the bending depends upon the total upward force and its distribution and is not simply related to magma viscosity as has been suggested by several previous investigators.After elastic bending strata should fail over the periphery of an intrusion, the site of maximum bending strain and differential stress predicted by the theory. Field observations described in Part I correlate well with these predictions. Because bending strains are proportional to layer thickness, strata of comparable strength but different thicknesses fail at different stages of laccolith development. This leads to the different cross-sectional forms of laccoliths observed in the field.The effect of host rocks on sill form and growth is analyzed using the elastic solution for an elliptical hole under uniform pressure. The theory suggests that sill thickness increases in proportion to length. The concentration of high stresses near the sill termination should induce permanent deformation and account for the blunt terminations described in Part I. This blunting is most likely to occur in relatively ductile rocks whereas sills simply split brittle rocks and maintain sharp terminations. The driving pressure in sills can be calculated from measurements of length and termination radius of curvature, if the yield strength of the host rocks can be estimated. This driving pressure must be greater than the overburden pressure, but sills apparently do not form or propagate by lifting their overburdens. Instead they propagate by locally deforming the host rock. After spreading over a distance about three times the effective overburden thickness, the overlying layers begin to bend upward significantly. This stage marks the transition from a sill to a laccolithic intrusion. 相似文献
14.
15.
Summary Mechanisms of flexural toppling failure of slopes in foliated rock masses are investigated both experimentally by testing
small scaled models in a centrifuge and theoretically by using a limiting equilibrium model and a finite element model based
on the Cosserat theory. Both theoretical models include bending moments of rock layers in their formulation. Two main failure
mechanisms are observed: (1) instantaneous failure involving a large volume of failed material and (2) progressive failure
where the fracture initially localises near the toe region and then progresses further into the rock mass with increasing
load. These two mechanisms of slope failure are observed to be controlled by the magnitude of the joint friction angle. The
joint friction angles of about 20° and above are most likely to cause instantaneous failure while the lesser friction angles
result in a progressive failure. Joint cohesion is not found to have a similar effect on the failure mechanisms, provided
that it is low enough to allow sliding between the rock layers – a prerequisite for flexural toppling. 相似文献
16.
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. 相似文献
17.
以白云鄂博露天铁矿东矿岩质高边坡为工程背景,结合现场地质调查、室内岩石和节理力学试验等数据,采用等效岩体技术,构建能充分反映节理分布特征的实验室、现场原位试验和工程尺度等多尺度等效岩体模型。通过对各类等效岩体模型进行单轴压缩试验,研究岩体单轴抗压强度、弹性模量等力学特性的尺寸效应和各向异性。研究表明：节理的存在使岩体表现出尺寸效应和各向异性,且随着尺寸的增大,这种特性基本呈逐渐减弱的趋势;研究区域岩体的表征单元体积、单轴抗压强度和弹性模量分别为20 m×10 m×10 m、1.46 MPa和3.91 GPa;岩体单轴抗压强度、弹性模量与轴向尺寸的关系,近似符合渐进式指数函数关系,且该函数能直观地给出工程尺度岩体的力学特性。 相似文献
18.
A thermomechanical anisotropic continuum model for geological materials with multiple joint sets 下载免费PDF全文
下载免费PDF全文 Joints in geological materials introduce elastic compliance and weak planes on which sliding can occur. Although these materials can have multiple joint sets, they often have preferred orientations that cause both elastic and inelastic anisotropic response even when the unjointed material is isotropic. Azimuthal variations in radial velocity and polarity of tangential motion have been observed in experimental data for wave propagation caused by an initially spherical source in a geological material with multiple joint sets. This observed tangential ground motion was found to be related to mechanical anisotropy caused by preferred orientations of joints in the rock. This paper describes thermomechanical continuum constitutive equations, which model the effects of multiple persistent joint sets. A number of quasi‐static examples are considered, which show that the proposed model predicts anisotropic effects of sliding on multiple joint sets similar to those exhibited by computationally expensive mesoscale calculations, which model joint sets explicitly. 相似文献
19.
Pierpaolo Oreste Giovanni Spagnoli Cesar Alejandro Luna Ramos Lisa Sebille 《Geotechnical and Geological Engineering》2018,36(4):2143-2169
Hyperstatic Reaction Method considers the interaction between the shotcrete lining and the rock mass modelling half tunnel section by beam elements connected by nodes, which can develop bending moments, axial forces and shear forces. The interaction between ground and support is represented by Winkler type springs in the nodes of the numerical model, in the normal and tangential direction. 1944 analyses were developed considering three different tunnel radius values (2.0, 4.5 and 7.0 m), three different rock types (RMR = 40, RMR = 60 and RMR = 80), three different stress ratios acting on the linings (\(K = 1, \,K = 0.5\) and \(K = 0\)), three different lining thickness values (0.1, 0.2 and 0.3 m) and three values of the average elastic modulus of the shotcrete (6000, 9000 and 12,000 MPa). Besides, also two different stiffness values of the tangential springs at nodes were considered. Results show that the lining thickness and the elastic modulus of the shotcrete have a strong influence on the bending moment values which develop inside. The maximum axial force is not practically influenced by the lining elastic modulus and thickness. Both maximum bending moments and maximum axial forces increase in a linear way with the vertical load value; tunnel radius, \(K\) and RMR values of the rock mass have also a great influence on the maximum bending moment and axial force. Besides, it is possible to note how the absence of shear interaction between the lining and the rock mass causes bending moment values in the lining higher with respect to the case where the stiffness of the tangential springs at nodes equals to half the stiffness of the normal springs. For this reason, the neglectance of the shear interaction between the lining and the tunnel wall leads to an overdesign of the SC lining. 相似文献