Evolution of induced fabric in a strain space multiple mechanism model for granular materials

The strain space multiple mechanism model idealizes the behavior of granular materials based on a multitude of virtual simple shear mechanisms oriented in arbitrary directions. Within this modeling framework, the virtual simple shear stress is defined as a quantity that depends on the contact distribution function as well as the normal and tangential components of inter‐particle contact forces, which evolve independently during the loading process. In other terms, the virtual simple shear stress is an intermediate quantity in the upscaling process from the microscopic level (characterized by the contact distribution and inter‐particle contact forces). The stress space fabric (i.e. the orientation distribution of the virtual simple shear stress) produces macroscopic stress through the tensorial average. Thus, the stress space fabric characterizes the fundamental and higher modes of anisotropy induced in granular materials. Comparing an induced fabric associated with the biaxial shear of plane granular assemblies obtained via a simulation using Discrete Element Method to the strain space multiple mechanism model suggests that the strain space multiple mechanism model has the capability to capture the essential features in the evolution of an induced fabric in granular materials. Copyright © 2012 John Wiley & Sons, Ltd.     

Induced fabric under cyclic and rotational loads in a strain space multiple mechanism model for granular materials

The strain space multiple mechanism model idealizes the behavior of granular materials on the basis of a multitude of virtual simple shear mechanisms oriented in arbitrary directions. Within this modeling framework, the virtual simple shear stress is defined as a quantity dependent on the contact distribution function as well as the normal and tangential components of interparticle contact forces, which evolve independently during the loading process. In other terms, the virtual simple shear stress is an intermediate quantity in the upscaling process from the microscopic level (characterized by contact distribution and interparticle contact forces) to the macroscopic stress. The stress space fabric produces macroscopic stress through the tensorial average. Thus, the stress space fabric characterizes the fundamental and higher modes of anisotropy induced in granular materials. Herein, the induced fabric is associated with monotonic and cyclic loadings, loading with the rotation of the principal stress, and general loading. Upon loading with the rotation of the principal stress axis, some of the virtual simple shear mechanisms undergo loading whereas others undergo unloading. This process of fabric evolution is the primary cause of noncoaxiality between the axes of principal stresses and strains. Although cyclic behavior and behavior under the rotation of the principal stress axis seem to originate from two distinct mechanisms, the strain space multiple mechanism model demonstrates that these behaviors are closely related through the hysteretic damping factor. Copyright © 2011 John Wiley & Sons, Ltd.     

A micromechanics-based model for estimating localized failure with effects of fabric anisotropy

This paper presents a micromechanics-based approach to investigate the effects of fabric anisotropy on the behavior of localized failure in granular materials. Based on a micromechanical analysis, the origin of deviatoric stress is decomposed into two components: contact force anisotropy and fabric anisotropy. Using a micro–macro approach, the back stress is interpreted as an contribution to the change of the fabric’s principal direction. The evolution of the back stress is deduced from the stress–fabric relationship and determined with reference to the deviation of the principal directions between the rate of the reduced stress tensor and the actual reduced stress tensor. With this micro–macro framework, a mixed (isotropic–kinematic) hardening model is developed based on the classical isotropic hardening theory. A laboratory simple shear test is first analyzed to validate the proposed model and illustrate the kinematic-hardening mechanism which is usually displayed under non-proportional loading. The analysis further focuses on the anisotropic aspect of localized failure. It has been discovered that the fabric anisotropy can play an important role in the occurrence of shear banding. An increasing degree of fabric anisotropy tends to delay the initiation of the strain localization and result in higher failure strength. The effects of fabric anisotropy have also been illustrated by comparing the theoretical predictions and measured results on the shear band inclination angle, shear strain level and dilatancy at bifurcation.     

Constitutive modeling of inherent anisotropy in a strain space multiple mechanism model for granular materials

Consideration of fabric anisotropy is crucial to gaining an improved understanding of the behavior of granular materials. This paper presents a constitutive model to describe the sand behavior associated with fabric anisotropy within a framework of a strain space multiple mechanism model. In the proposed model, a second-order fabric tensor is extended by incorporating a new function that represents the effect of inherent (or initial fabric) anisotropy, along with three additional parameters: two of them, a₁ and a₂ , control the degree of anisotropy, and the second mode of inherent anisotropy can be expressed by introducing the parameter a₂ as well as the first mode by the parameter a₁ . The third parameter, θ₀ , expresses the principal direction of inherent anisotropy (eg, the normal vector direction of bedding planes relative to horizontal axis). The formulation of the dilative component of dilatancy (ie, positive dilatancy) is also extended to consider the effect of inherent anisotropy based on the interlocking mechanism. Experimental data on the complex anisotropic responses of Fraser River sand and Toyoura sand under monotonic loading is used to validate this model. The proposed model is shown to successfully capture anisotropic responses, which become contractive or dilative depending on different principal-stress directions, with a single set of anisotropy parameters; thus, the model is considered to possess the capability to simulate the anisotropic behaviors of granular materials. In addition to different loadings on the same fabric, the effects of different fabric anisotropies upon the sand behavior under the same loadings are also investigated.     

粗粒土与结构接触面的可逆性与不可逆性剪胀规律

进行了粗粒土与结构接触面的单调和往返剪切试验,研究了接触面的剪胀特性。试验结果表明,接触面的剪胀体应变是由一个完全可逆性的体应变分量和一个不可逆性的体应变分量构成的。不可逆性剪胀体应变反映了接触面内的土颗粒破碎和剪切压密两种物态变化,其变化规律与接触面的应力相对位移关系的演化规律具有相似性,是接触面力学特性演化的一个重要量度。可逆性剪胀体应变存在相变点,并表现出明显的剪切异向性,该异向性的主要内因是由于剪切引起的结构面附近土的结构异向性。基于接触面受力变形机理分析,引入有效剪应变等概念,建立了剪胀方程。     

考虑应变局部化的粗粒料剪切损伤力学机制

针对粗粒料的应变软化、剪胀等力学特性,通过考虑以剪切带为标志的应变局部化现象,建立了具有广泛适用性的剪切损伤力学模型。损伤模型采用了包体理论中的剪切带数学简化,基于应变等价原理、Weibull分布,推导了粗粒料的应力-应变关系方程。从剪胀作用的机制出发,提出可以描述剪胀弱化的轴向塑性应变和体积塑性应变的非线性函数关系。结合粗粒料三轴压缩试验中的伺服过程,提出了基于遗传算法的损伤模型参数确定方法。通过开展不同围压下的粗粒料三轴压缩试验,对剪切损伤力学模型进行验证,进一步分析了参数演化对粗粒料强度和变形特征的影响。研究结果表明,考虑应变局部化特征的剪切损伤力学模型可以高精度的模拟粗粒料的应变软化和剪胀等特征,有效揭示剪切带内部变形对试样整体宏观变形的影响机制,模型中剪切带参数和围压的关系与粗粒料细观机制一致,计算得到强度组成与颗粒破碎、重组特征较为吻合。     

颗粒材料的微观临界状态理论模型

存在临界状态是颗粒材料的一个重要特性。基于孔隙胞元的颗粒离散元方法对二维颗粒体进行双轴加载数值试验,在详细分析数值模拟结果的基础上,从微观几何组构的角度揭示了临界状态的存在机制。基于剪胀性原理,提出了以接触价键表征的微观临界状态理论模型,得到了接触价键与塑性剪切应变的关系表达式,理论模型的结果和二维离散元数值模拟得到的结果吻合较好。通过比较不同情况下数值结果和理论模型中的参数,得到以下结论：表征微观临界状态的参数（临界接触价键和达到临界状态所需要的塑性剪切应变）依赖于颗粒体的微观特性,如颗粒形状、表面摩擦性质、颗粒体的围压和初始孔隙比。     

砂土多机构边界面塑性模型及其试验验证

根据Iai多重剪切机构塑性模型及边界面塑性模型的特点,建立了一个砂土多机构边界面塑性模型。该模型将土复杂的变形机理分解为体积机理和一系列简单的剪切机理。用边界面弹塑性模型模拟多重剪切机构塑性模型中虚拟单剪机构,避免了Iai多重剪切机构塑性模型在利用修正Masing准则模拟虚拟单剪应力-应变关系时确定比例参数的复杂性。根据大量试验资料,建立了液化面参数与归一累积剪切功的关系,能够用较少的参数很好地建立有效应力路径。由于多重机理的特性,该模型能够模拟复杂荷载作用下主应力轴偏转的影响。试验结果表明,应用该模型的计算结果与试验结果有较好的一致性。     

Particle shape effect on macro‐ and micro‐behaviors of monodisperse ellipsoids

The microscopic and macroscopic behaviors of assemblages of monodisperse ellipsoids with different particle shapes were studied using the discrete element method. Four samples were created with 1170 identical prolate ellipsoids. The samples were compressed isotropically to 100 kPa. Then triaxial compression tests were carried out to very large strains until the ultimate state was reached. This paper presents typical macroscopic result including stress–strain relationship and volumetric behavior. In addition, the fabric of the samples was examined at the initial state, at the peak shear strength state, and at the ultimate state. We studied the evolution of three vector‐typed micromechanical arguments with strain including the particle orientation, branch vector, and normal contact force. The normal contact force (micromechanical argument) was found to have a direct relationship with the principal stress ratio (macroscopic parameter). The angles between these vectors were also investigated. The maximum angle between vectors is related to particle shape. The results indicate that the distributions and the maximum values of these angles do not change with loading. Copyright © 2008 John Wiley & Sons, Ltd.     

Experimental analysis of kaolinite particle orientation during triaxial path

The goal of this study was to analyze the relation between the behaviour of a clayey material at the macroscopic scale and its microfabric evolution. This may lead to a better understanding of macroscopic strain mechanisms especially the contractancy and dilatancy phenomena. The approach proposed in this paper is based on the study of clay particles orientation by SEM picture analysis after different phases of triaxial loading. In the initial state of the samples (one‐dimensional compression), the SEM observations highlight a microstructural anisotropy with a preferential orientation of the particles normal to the loading direction. During isotropic loading, densification of the clayey matrix occurs related to a random orientation of particles indicated by the term ‘depolarization’. In the earlier stages of constant σ₃ drained triaxial path on slightly overconsolidated specimens, the microstructural depolarization seems to persist inside a macroscopic domain, in which only the volumetric strains due to the isotropic part of the stress tensor evolve. Then, a rotation mechanism of the particles towards preferred directions seems to be activated. The phenomenon appears directly linked to the evolution of the deviatoric part of the stress tensor. Copyright © 2010 John Wiley & Sons, Ltd.     

初始组构各向异性对砂土力学特性及临界状态的影响

采用离散元方法,利用半径扩展法和重力沉积法分别生成具有初始各向同性和各向异性内结构的试样,并开展三轴不排水压缩和拉伸试验,研究不同制样方法产生的初始各向异性对砂土宏微观力学特性及其临界状态的影响。运用组构张量对砂土的各向异性进行量化,分析不同初始组构各向异性对组构张量演化的影响并确定了组构张量的临界值。试验结果表明：初始组构各向异性对试样的剪胀性有重要影响,由于受重力影响形成初始各向异性,其各向异性程度越大、组构方向与加载方向越一致,剪胀性越显著;初始组构各向异性对试样的临界状态没有影响,砂土的组构张量具有唯一的临界状态值。     

Micromechanical aspects of the shear strength of wet granular soils

This paper presents a micromechanical model for the analysis of wet granular soils at low saturation (below 30%). The discrete element method is employed to model the solid particles. The capillary water is assumed to be in a pendular state and thus exists in the form of liquid bridges at the particle‐to‐particle contacts. The resulting inter‐particle adhesion is accounted for using the toroidal approximation of the bridge. Hydraulic hysteresis is accounted for based on the possible mechanism of the formation and breakage of the liquid bridges during wetting and drying phases. Shear test computational simulations were conducted at different water contents under relatively low net normal stresses. The results of these simulations suggest that capillary‐induced attractive forces and hydraulic hysteresis play an important role in affecting the shear strength of the soil. These attractive forces produce a tensile stress that contributes to the apparent cohesion of the soil and increases its stiffness. During a drying phase, capillary‐induced tensile stresses, and hence shear strength, tend to be larger than those during a wetting phase. The proposed model appears to capture the macroscopic response of wet granular materials and revealed a number of salient micromechanical mechanisms and response patterns consistent with theoretical considerations. Copyright © 2008 John Wiley & Sons, Ltd.     

Discrete element modelling of material non‐coaxiality in simple shear flows

We investigate the quasi‐static simple shear flow of a two‐dimensional assembly of cohesionless particles using discrete element method (DEM) simulations. We focus on the unsteady flow regime where the solid would experience significant evolution of stresses, mobilised shear strength and dilation. We construct the DEM model using a discretised‐wall confined granular cell where the apparent boundary is allowed to dilate or contract synchronously with the confined solid. A rather uniform simple shear field is achieved across the whole assembly, which benefits rheological studies in generalising constitutive laws for continuum methods. We examine two aspects of the simple shear behaviour: macroscopic stress and strain rate evolution, particularly the non‐coaxiality between the principal directions of the two; and micromechanics such as evolution of fabric. For an initially anisotropic specimen sheared under constant normal pressure, the direction of principal stress rotates towards that of the principal strain rate, gradually reducing the degree of non‐coaxiality from about 45° to fluctuating around 0°. The rate in approaching coaxiality is slower in samples with larger initial porosity, stress ratio and mean stress. Generally, a faster rate in approaching coaxiality in simple shear is observed in a more dilatant sample, which often shows a larger degree of mobilised fabric anisotropy, suggesting the possible important role of instantaneous internal friction angle. The evolution of principal fabric direction resembles that of the principal stress direction. © 2013 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons, Ltd.     

Analysis of soil‐structural interface behavior using three‐dimensional DEM simulations

The shear behavior at the interface between the soil and a structure is investigated at the macroscale and particle‐scale levels using a 3‐dimensional discrete element method (DEM). The macroscopic mechanical properties and microscopic quantities affected by the normalized interface roughness and the loading parameters are analyzed. The macro‐response shows that the shear strength of the interface increases as the normalized roughness of the interface increases, and stress softening and dilatancy of the soil material are observed in the tests that feature rough interfaces. The particle‐scale analysis illustrates that a localized band characterized by intense shear deformation emerges from the contact plane and gradually expands as shearing progresses before stabilizing at the residual stress state. The thickness of the localized band is affected by the normalized roughness of the interface and the normal stress, which ranges between 4 and 5 times that of the median grain diameter. A thicker localized band is formed when the soil has a rough shearing interface. After the localized band appears, the granular material structuralizes into 2 regions: the interface zone and the upper zone. The mechanical behavior in the interface zone is representative of the interface according to the local average stress analysis. Certain microscopic quantities in the interface zone are analyzed, including the coordination number and the material fabric. Shear at the interface creates an anisotropic material fabric and leads to the rotation of the major principal stress.     

On the capillary stress tensor in wet granular materials

This paper presents a micromechanical study of unsaturated granular media in the pendular regime, based on numerical experiments using the discrete element method, compared with a microstructural elastoplastic model. Water effects are taken into account by adding capillary menisci at contacts and their consequences in terms of force and water volume are studied. Simulations of triaxial compression tests are used to investigate both macro and micro‐effects of a partial saturation. The results provided by the two methods appear to be in good agreement, reproducing the major trends of a partially saturated granular assembly, such as the increase in the shear strength and the hardening with suction. Moreover, a capillary stress tensor is exhibited from capillary forces by using homogenization techniques. Both macroscopic and microscopic considerations emphasize an induced anisotropy of the capillary stress tensor in relation with the pore fluid distribution inside the material. Insofar as the tensorial nature of this fluid fabric implies shear effects on the solid phase associated with suction, a comparison has been made with the standard equivalent pore pressure assumption. It is shown that water effects induce microstructural phenomena that cannot be considered at the macro level, particularly when dealing with material history. Thus, the study points out that unsaturated soil stress definitions should include, besides the macroscopic stresses such as the total stress, the microscopic interparticle stresses such as the ones resulting from capillary forces, in order to interpret more precisely the implications of the pore fluid on the mechanical behaviour of granular materials. Copyright © 2009 John Wiley & Sons, Ltd.     

砂土的物态本构模型

基于砂土的压缩回胀性、剪切非线性及剪缩剪胀性的系统分析和包括循环荷载、主应力轴旋转及应力路径偏转等复杂应力条件下的复杂变形反应,得到了三类应力-应变基本关系。在剪缩剪胀应力-应变关系中,引入了由偏应变分量确定的应变路径长度变量,揭示了应力主轴旋转、应力路径偏转引起的剪缩剪胀性。将这些基本关系与循环荷载下砂土的物态变化相联系,建立了砂土的物态动本构关系。     

On the role of particle breakage in the shear failure behavior of granular soils by DEM

This article presents a fundamental study on the role of particle breakage on the shear behavior of granular soils using the three‐dimensional (3‐D) discrete element method. The effects of particle breakage on the stress ratio, volumetric strain, plastic deformation, and shear failure behavior of dense crushable specimens undergoing plane strain shearing conditions are thoroughly investigated through a variety of micromechanical analyses and mechanism demonstrations. The simulation of a granular specimen is based on the effective modeling of realistic fracture behavior of single soil particles, which is demonstrated by the qualitative agreement between the results from platen compression simulations and those from physical laboratory tests. The simulation results show that the major effects of particle breakage include the reduction of volumetric dilation and peak stress ratio and more importantly the plastic deformation mechanisms and the shear failure modes vary as a function of soil crushability. Consistent macro‐ and micromechanical evidence demonstrates that shear banding and massive volumetric contraction depict the two end failure modes of a dense specimen, which is dominated by particle rearrangement–induced dilation and particle crushing–induced compression, respectively, with a more general case being the combination and competition of the two failure modes in the medium range of soil crushability and confining stress. However, it is further shown that a highly crushable specimen will eventually develop a shear band at a large strain because of the continuous decay of particle breakage. Copyright © 2011 John Wiley & Sons, Ltd.     

On double shearing in frictional materials

This paper evaluates the mechanical behaviour of yielding frictional geomaterials. The general Double Shearing model describes this behaviour. Non‐coaxiality of stress and plastic strain increments for plane strain conditions forms an important part of this model. The model is based on a micro‐mechanical and macro‐mechanical formulation. The stress–dilatancy theory in the model combines the mechanical behaviour on both scales. It is shown that the general Double Shearing formulation comprises other Double Shearing models. These models differ in the relation between the mobilized friction and dilatancy and in non‐coaxiality. In order to describe reversible and irreversible deformations the general Double Shearing model is extended with elasticity. The failure of soil masses is controlled by shear mechanisms. These shear mechanisms are determined by the conditions along the shear band. The shear stress ratio of a shear band depends on the orientation of the stress in the shear band. There is a difference between the peak strength and the residual strength in the shear band. While peak stress depends on strength properties only, the residual strength depends upon the yield conditions and the plastic deformation mechanisms and is generally considerably lower than the maximum strength. It is shown that non‐coaxial models give non‐unique solutions for the shear stress ratio on the shear band. The Double Shearing model is applied to various failure problems of soils such as the direct simple shear test, the biaxial test, infinite slopes, interfaces and for the calculation of the undrained shear strength. Copyright © 2006 John Wiley & Sons, Ltd.     

Quartz fabrics in shear-zone mylonites: Evidence for a major imprint due to late strain increments

Geometrical relations between quartz C-axis fabrics, textures, microstructures and macroscopic structural elements (foliation, lineation, folds…) in mylonitic shear zones suggest that the C-axis fabric mostly reflects the late-stage deformation history. Three examples of mylonitic thrust zones are presented: the Eastern Alps, where the direction of shearing inferred from the quartz fabric results from a late deformation oblique to the overall thrusting; the Caledonides nappes and the Himalayan Main Central Thrust zone, where, through a similar reasoning, the fabrics would also reflect late strain increments though the direction of shearing deduced from quartz fabric remains parallel to the overall thrusting direction. Hence, the sense of shear and the shear strain component deduced from the orientation of C-axis girdles relative to the finite strain ellipsoid axes are not simply related nor representative of the entire deformation history.