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.     

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.     

泥岩夹层对层状盐岩体中储库稳定性影响

针对盐矿常为不同岩层交替而成的互层盐岩体的基本特点,利用宏观平均意义下考虑细观弯曲效应的三维Cosserat介质扩展本构模型的FLAC3D接口程序,对湖北云应地区的ZK1075,ZK1083,ZK1099溶腔进行了计算,不仅考虑了刚度异于盐岩的泥岩对复合体弹性特征的影响,并且考虑了由于各层内部位移协调引起泥岩夹层先行破损,进而引起复合体变形和破坏。计算结果表明,云应地区的层状盐岩体中的刚度、强度较大的泥岩夹层对层状盐岩复合体具有强化作用,对盐岩溶腔造腔后的稳定性有利。     

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.     

Numerical Simulation of Bed Separation Development and Grout Injecting into Separations

In this paper, the Cosserat theory that has been incorporated into a three dimensional finite element code COSFLOW, is applied to analyze the development of bed separations in the layered overburden and grout injection into the bed separations. The mechanism of bed separation development during the longwall mining is investigated. A parametric study is carried out to investigate the effect of major factors including hard rock grade, panel height and panel weight on bed separation development. Based on the modeling, a conceptual model to describe the development process of bed separation is proposed. The effect of grout injecting into the bed separations on subsidence reduction is also studied and the conclusion agrees well with the common realization.     

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.     

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。     

Modelling of Progressive and Instantaneous Failures of Foliated Rock Slopes

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.     

On a new law of faulting along tectonic wedges: Cosserat explanation of the preferred (paleo)stress states in the Earth's crust

Cosserat extension of the Gauss stress-strain inversion method and multiple-slip method (MSM) are used to analyse 18 examples of natural wedge faulting observed in Slovenia. Based on additional numerical tests we show that kinematic incompatibility of slip along intersecting faults (wedges) has a significant effect on the state of stress in the Earth's crust. The slip direction along intersecting faults (wedges) can only be subparallel to the intersection direction between the faults. The normal stress on the wedges is then equal to the intermediate principal stress (eigenvalue) of the symmetric part of the stress tensor. This equality is very fundamental and could potentially be interpreted as a new law of faulting along tectonic wedges and non-planar faults. In the Cosserat theory of wedge faulting we also define two stress criteria, these are the weak and the strong stress conditions. The weak stress condition is related to the frictional reactivation of the wedges. It defines two limit values of the stress parameter and intermediate principal stress of the symmetric part of the stress tensor. The strong stress condition is related to the brittle faulting along tectonic wedges. It relates the angle of internal friction to the value of the stress parameter and the intermediate principal stress of the symmetric part of the stress tensor. For the value of the angle of internal friction larger than zero, the stress parameter is less than 0.5, which is in agreement with numerical and empirical observations described in this paper.