Numerical studies of shear banding in interface shear tests using a new strain calculation method

Strain localization is closely associated with the stress–strain behaviour of an interphase system subject to quasi‐static direct interface shear, especially after peak stress state is reached. This behaviour is important because it is closely related to deformations experienced by geotechnical composite structures. This paper presents a study using two‐dimensional discrete element method (DEM) simulations on the strain localization of an idealized interphase system composed of densely packed spherical particles in contact with rough manufactured surfaces. The manufactured surface is made up of regular or irregular triangular asperities with varying slopes. A new simple method of strain calculation is used in this study to generate strain field inside a simulated direct interface shear box. This method accounts for particle rotation and captures strain localization features at high resolution. Results show that strain localization begins with the onset of non‐linear stress–strain behaviour. A distinct but discontinuous shear band emerges above the rough surface just before the peak stress state, which becomes more expansive and coherent with post‐peak strain softening. It is found that the shear bands developed by surfaces with smaller roughness are much thinner than those developed by surfaces with greater roughness. The maximum thickness of the intense shear zone is observed to be about 8–10 median particle diameters. The shear band orientations, which are mainly dominated by the rough boundary surface, are parallel with the zero extension direction, which are horizontally oriented. Published in 2007 by John Wiley & Sons, Ltd.     

Micro-mechanical analysis of soil–structure interface behavior under constant normal stiffness condition with DEM

The mechanical behavior at soil–structure interface (SSI) has a crucial influence on the safety and stability of geotechnical structures. However, the behavior of SSI under constant normal stiffness condition from micro- to macro-scale receives little attention. In this study, the frictional characteristics of SSI and the associated displacement localization under constant normal stiffness condition are investigated at both macro- and microscales by simulating a series of interface shear tests with discrete element method. The algorithm to achieve a constant normal stiffness is first developed. The macroscopic mechanical response of the interface shear tests with both loose and dense specimens at various normal stiffness is discussed in terms of shear stress, normal stress, vertical displacement, horizontal displacement and stress ratio. Then, the microscopic behaviors and properties, including shear zone formation, localized void ratio, coordination number, force chains and soil fabric, are investigated. The effect of normal stiffness is thus clarified at both macro- and microscales.

     

Observations on fabric evolution to a common micromechanical state at the soil-structure interface

The fabric plays an important role in the mechanical behavior of granular material. The aim of this paper is to investigate the evolution of fabric in a soil-structure interface (SSI) to a large shearing in an effort to clarify whether and how this form of fabric evolution can lead to a common microstructure. Using the discrete element method (DEM), two-dimensional (2D) numerical interface shear tests were carried out, and certain macromechanical and micromechanical properties were exploited. All samples exhibited prominently localized strain in a zone covering the structure's surface (named the localized zone), and much lower density and higher soil fabric anisotropy levels were found inside this zone than outside it. Disregarding different initial void ratios, a common critical state microstructure was observed in large shear deformations of soil samples, with essentially the same fabric arrangement in terms of contact orientation and internal force transmission. Due to the systematic forming, buckling, and collapsing of force chains, an angular zone (called an α -zone), in which contact density was sluggish to varying degrees, appeared and extended around the main direction of the distribution of contact orientation inside the localized zone. The gradual deterioration of the force chains' stability, as a result of an increasing void ratio, seemed to drive the α -zone's extension and lead to the rare variation of microstructures in the critical state.     

平均粒径对砂土剪切特性的影响及细观机理

针对平均粒径对砂土剪切特性的影响作用,结合室内试验和离散元模拟方法对不同平均粒径砂土进行了细观研究。基于3种不同平均粒径砂土的直剪试验结果,通过建立反映砂土剪切试验特征的PFC（particle flow code）颗粒流模型,详细研究了不同粒径砂土在剪切过程中土样体积变化、力链网络、孔隙率和配位数等细观结构参数的变化特征和规律,并从细观角度分析了颗粒粒径对土样宏观剪切特性的影响机制。结果表明：具有不同平均粒径砂土的细观结构参数在剪切过程中存在显著差异,并且其细观参数差异主要集中体现在剪切带处;剪切力学特性的影响主要体现在抗剪强度和剪胀效应方面,砂土平均粒径越大,抗剪强度越高,剪胀效应越明显;具有不同平均粒径的砂土在剪切过程中土颗粒运动规律及剪切带形态变化特征存在一定的差异,平均粒径越大,剪切带内上跨式颗粒占比越大,剪切带厚度越大。     

Particle‐scale effects on global axial and torsional interface shear behavior

An extensive literature on the shear behavior of continuum–particulate interfaces has been developed during the last four decades. However, relatively limited work regarding the behavior of interfaces under different loading conditions has been published. This paper presents a discrete element modeling study, along with comparisons from experimental data, of interface behavior under axial and torsional drained loading conditions. Detailed studies allow for links between micro‐scale particle behavior and observed global response to be developed and for the latter to be evaluated in light of particle–particle and particle–continuum interactions. The results of this study indicate that axial and torsional interface shear induce inherently different loading conditions, as shown by the different failure envelopes, stress paths, and induced soil volume changes and deformations. Furthermore, the results presented in this paper indicate that particle‐level mechanisms, such as particle rotations and contact slippage, play different roles in axial and torsional shear. Coordination number, polar histograms, particle displacements, particle rotations, and local void ratio measurements provide further insights into the fabric evolution, loading conditions, and failure mechanisms induced by these two shear modes. This study expands the current understanding of interface behavior and discusses potential improvements to geotechnical systems that leverage the characteristics of different imposed loading conditions. Copyright © 2016 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.     

基于离散元法的砂土破碎演化规律研究

颗粒破碎是影响砂土宏-微观力学性质的重要因素。采用改进型的可破碎颗粒生成方法,通过设置不同强度的平行黏结键模拟不同强度的可破碎颗粒,并借用基于离散元方法（DEM）的双轴压缩试验详细研究了可破碎性土在剪切过程中颗粒破碎率/平均破碎程度、微观尺度上的能量耗散分配机制、剪切破碎带形成以及断裂键各向异性的演化过程。结果表明,颗粒破碎强烈地影响砂土在宏观尺度上的力学响应、颗粒尺度上的能量分配机制以及剪切过程中的颗粒的组织结构演化。颗粒破碎主要影响小应变阶段各能量耗散元的分配机制,而在临界状态下剪切带内的颗粒摩擦以及破碎耗能是消耗外界功的主要因素。数值结果亦表明,颗粒的破碎伴随着整个剪切过程,但破碎率的增长速度却随着剪切应变的发展逐渐降低。另外,在剪切过程中,对于低破碎性土,在临界状态下剪切破碎带基本形成,带内的原有组织结构被打乱,断裂键的各向异性也随之弱化。     

Deformation mechanism of strain localization in 2D numerical interface tests

Heterogeneity arises in soil subjected to interface shearing, with the strain gradually localizing into a band area. How the strain localization accumulates and develops to form the structure is crucial in explaining some significant constitutive behaviors of the soil–structural interface during shearing, for example, stress hardening, softening, and shear-dilatancy. Using DEM simulation, interface shear tests with a periodic boundary condition are performed to investigate the strain localization process in densely and loosely packed granular soils. Based on the velocity field given by grains’ translational and rotational velocities, several kinematic quantities are analyzed during the loading history to demonstrate the evolution of strain localization. Results suggest that tiny concentrations in the shear deformation have already been observed in the very early stage of the shear test. The degree of the strain localization, quantified by a proposed new indicator, α, steadily ascends during the stress-hardening regime, dramatically jumps prior to the stress peak, and stabilizes at the stress steady state. Loose specimen does not develop a steady pattern at the large strain, as the deformation pattern transforms between localized and diffused failure modes. During the stress steady state of both specimens, remarkable correlations are observed between α and the shear stress, as well as between α and the volumetric strain rate.     

粗粒土大型剪切试验剪切带变形特征分析

采用含有叠环的大型粗粒土直剪试验设备进行试验,叠环作为剪切盒的重要组成部分,可以在剪切时根据粗粒土的结构形成多组剪切面,能够明显地展现出粗粒土的剪切变形特征.为了分析硬质岩粗粒对粗粒土的剪切强度和变形的影响,对粗粒岩性为花岗岩的粗粒土进行大型叠环式直剪试验.通过分析得到试验特征规律,研究粗粒土在剪切过程中的颗粒运动,得出花岗岩粗粒对其组成的粗粒土的剪切强度和变形有很大的影响.硬质岩性的花岗岩颗粒在剪切时不易被剪碎,在剪切过程中主要做错位、翻滚运动.低轴压下,剪切带位移会出现阶梯现象,而在高轴压下,剪切带位移为线性变化,并表现出更加明显的剪胀现象.粗粒土在剪切破坏后依然具有较高的抗剪强度和稳定性,为工程建设中土石体材料的选取提供了一定的借鉴.     

Experimental Investigation of Frictional Behavior Between Cohesive Soils and Solid Materials Using Direct Shear Apparatus

Soil shearing resistance is very important while designing various structures which have direct contact with soil, for example, sheet piles, piles, retaining walls, reinforced earth structures and shallow foundations. Even though designers use empirical values for their design, it is very important to obtain more accurate values for soil–solid materials shearing resistance. In this work, laboratory tests have been carried out to investigate the effect of roughness interface and texture models on friction angle between cohesive soils and steel, as well as abrasive paper material, using direct shear tests. All tests were carried out under consolidated drained shear conditions. The behavior at the soils–solid interface was found to vary according to surface roughness. It also seems that the type of material (steel or paper of abrasive) used does not have a major influence on the shear strength. As far as roughness is concerned, friction behavior is likely to be generally classified into three failure modes, namely full sliding at the interface, shear failure within the soil, and a mixed behavior where interface sliding and shear deformation of the soil specimen proceed simultaneously. However, for the second mode, the shear strength at the interface soil-rough solid materials steel was found to be lower than the shear strength of the soil, for a soil that is classified as high plasticity clay. Furthermore, it was found that the interfacial shear strength is independent of the texture surface for a given roughness.     

A micro‐mechanical study of peak strength and critical state

We present a micro‐mechanical analysis of macroscopic peak strength, critical state, and residual strength in two‐dimensional non‐cohesive granular media. Typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain‐scale counterparts (e.g., inter‐particle contact forces, fabric, particle displacements, and velocities), providing an across‐the‐scale basis for a better understanding and modeling of granular materials. These multi‐scale relations are derived in three steps. First, explicit relations between macroscopic stress and strain rate with the corresponding grain‐scale mechanics are established. Second, these relations are used in conjunction with the non‐associative Mohr–Coulomb criterion to explicitly connect internal friction and dilation angles to the micro‐mechanics. Third, the mentioned explicit connections are applied to investigate, understand, and derive micro‐mechanical conditions for peak strength, critical state, and residual strength. Copyright © 2015 John Wiley & Sons, Ltd.     

不同环剪方式下滑带土残余强度试验研究

以三峡库区黄土坡滑坡滑带土为研究对象,利用环剪仪研究了黄土坡滑坡滑带土在单级剪、预剪以及多级剪3种环剪方式下的残余强度特征。试验结果表明：不同环剪试验下剪切带的形成与剪切位移相关;残余强度随有效法向应力的增大而增大,对于已经存在剪切带的滑带土,环剪时能很快达到残余强度状态;滑带土环剪轴向压缩分初始剪胀、颗粒运移压密和稳定压密3个阶段,且每个阶段剪应力变化趋势不同;预剪试验和多级剪切试验得到的残余强度偏大,应该首选单级剪切试验测试滑带土残余强度指标。     

颗粒形状对粗粒土剪切变形影响的细观研究

颗粒形状是影响粗粒土密实度、力学与渗流等特性的主要因素之一。为了分析颗粒形状对粗粒土剪切特性的影响,采用离散元法生成4种不同形状的颗粒组,进行粗粒土直剪试验模拟与剪切宏细观响应研究,得出了颗粒形状对剪应力-剪位移、体应变-剪位移的影响,分析了粗粒土剪切应力、应变特性与剪胀特性。通过分析剪切带厚度、颗粒旋转量值、平均接触数、孔隙率及接触力系等宏细观参量的演化规律,研究颗粒形状在宏细观尺度上对粗粒土的影响。研究表明:异形颗粒间的咬合自锁作用大于纯圆颗粒,试样的抗剪强度有随形状系数的减小而增大的趋势。试样颗粒在外荷载作用下发生运动,应变主要表现在颗粒运动剧烈、剪胀幅度较大的剪切带内。颗粒形状系数F减小,试样的初始平均接触数增加,内摩擦角φ增大,剪切带内孔隙率增量越大,剪胀幅度越大。剪切过程中强力链聚集于剪切带内并起骨架作用,随着形状系数的减小,力链长度在0～5所占百分比呈增大趋势;剪切带内强力链的数目随着形状系数的减小而增加,峰值含量在30%～35%之间。     

Numerical simulation of fabric anisotropy and strain localization of sand under simple shear

This paper studies the effects of initial fabric anisotropy of dry sand in simple shear deformation. The effects of anisotropy are taken into consideration through the modification of the mobilized friction in the Mohr–Coulomb‐type yield surface as a function of a fabric parameter. In addition, the constitutive model uses a gradient term that directly incorporates the effects of material length scale. The constitutive formulation is implemented into ABAQUS finite element code and used to simulate shearing of the dry sand under various conditions of simple shear. The numerical simulations show that while the shear stress response is affected by fabric anisotropy, its effects on strain localization in simple shear are minimal. This is in contrast to other devices such as the biaxial shear. The strain localization in simple shear is controlled more by the imposed boundary conditions. The use of material length scale is shown to remove the effects of strain localization in the shearing response. Copyright © 2009 John Wiley & Sons, Ltd.     

Macro‐and Microstructural,Textural Fabrics and Deformation Mechanism of Calcite Mylonites from Xar Moron‐Changchun Dextral Shear Zone,Northeast China

The calcite mylonites in the Xar Moron-Changchun shear zone show a significance dextral shearing characteristics. The asymmetric(σ-structure) calcite/quartz grains or aggregates, asymmetry of calcite c-axes fabric diagrams and the oblique foliation of recrystallized calcite grains correspond to a top-to-E shearing. Mineral deformation behaviors, twin morphology, C-axis EBSD fabrics, and quartz grain size-frequency diagrams demonstrate that the ductile shear zone was developed under conditions of greenschist facies, with the range of deformation temperatures from 200 to 300°C. These subgrains of host grains and surrounding recrystallized grains, strong undulose extinction, and slightly curved grain boundaries are probably results of intracrystalline deformation and dynamic recrystallization implying that the deformation took place within the dislocation-creep regime at shallow crustal levels. The calculated paleo-strain rates are between 10~(–7.87)s~(–1) and 10~(–11.49)s~(–1) with differential stresses of 32.63–63.94 MPa lying at the higher bound of typical strain rates in shear zones at crustal levels, and may indicate a relatively rapid deformation. The S-L-calcite tectonites have undergone a component of uplift which led to subhorizontal lifting in an already non-coaxial compressional deformation regime with a bulk pure shear-dominated general shear. This E-W large-scale dextral strike-slip movement is a consequence of the eastward extrusion of the Xing'an-Mongolian Orogenic Belt, and results from far-field forces associated with Late Triassic convergence domains after the final closure of the Paleo-Asian Ocean.     

考虑各向异性的原状软黏土微观结构变化机制研究

采用电镜扫描仪（SEM）对在复杂应力路径作用下剪切前后的黏土样进行微观观察,并从剪切前后孔隙排列、孔隙形态、孔隙尺度变化特征3方面分析宏观试验原状软黏土归一化抗剪强度各向异性的微观本质。试验表明：剪切前后孔隙排列无序,孔隙排列方向变化很小,对黏土宏观性质影响很小;当中主应力参数b=0时,剪切过程中孔隙形态的变化对剪切后黏土归一化抗剪强度表现出的各向异性贡献较大;当b =0.5时,剪切过程中孔隙尺度的变化对剪切后黏土归一化抗剪强度表现出的各向异性贡献较大。因此,当中主应力参数不同时,影响剪切后黏土归一化抗剪强度各向异性的土的微观变化因素不同。     

Strength anisotropy of granular material consisting of perfectly round particles

The strength anisotropy of granular materials deposited under gravity has mostly been attributed to elongated particles' tendency to align long axes along the bedding plane direction. However, recent experiments on near‐spherical glass beads, for which preferred particle alignment is inapplicable, have exhibited surprisingly strong strength anisotropy. This study tests the hypothesis that certain amount of fabric anisotropy caused by the anisotropic stress during deposition under gravity can be locked in a circular‐particle deposit. Such locked‐in fabric anisotropy can withstand isotropic consolidation and leads to significant strength anisotropy. 2D discrete element method simulations of direct shear tests on circular‐particle deposits are conducted in this study, allowing for the monitoring of both stress and fabric. Simulations on both monodispersed and polydispersed circular‐particle samples generated under downward gravitational acceleration exhibit clear anisotropy in shear strength, thereby proving the hypothesis. When using contact normal‐based and void‐based fabric tensors to quantify fabric anisotropy in the material, we find that the intensity of anisotropy is discernible but low prior to shearing and is dependent on the consolidation process and the dispersity of the sample. The fact that samples with very low anisotropy intensity measurements still exhibit fairly strong strength anisotropy suggests that current typical contact normal‐based and void‐based second‐order fabric tensor formulations may not be very effective in reflecting the anisotropic peak shear strength of granular materials. Copyright © 2017 John Wiley & Sons, Ltd.     

Non‐linear analysis of shear band formation in sand

The paper investigates the incipience of shear band with an incrementally non‐linear constitutive equation. Necessary conditions for the emergence of shear band are derived. The lower bound solution is obtained by taking the strain rate inside and outside the shear band into consideration. Numerical results of localized bifurcation for general stress and strain are presented and compared with experiments. In the principal stress space, the stresses at the onset of shear band form a surface, which is partially enclosed by the failure surface for homogeneous straining. The significance of the analysis for identification of the material parameters and verification of the constitutive model against experiments is discussed. Copyright © 2000 John Wiley & Sons, Ltd.     

Quantification of particle crushing in consideration of grading evolution of granular soils in biaxial shearing: A probability‐based model

A probability‐based model is presented to estimate particle crushing and the associated grading evolution in granular soils during isotropic compression and prepeak shearing in biaxial tests. The model is based on probability density functions of interparticle and intraparticle stress (ie, particle normalized maximum shear stress and particle average maximum shear stress) derived from discrete element method simulations of biaxial tests. We find that the probability density functions of normalized maximum shear stress are dependent on the current sample grading, implying coupling effects between particle crushing and sample grading such that the particle crushing is affected by the current sample grading, and the grading change is also dependent on the current particle crushing extent. To incorporate these coupling effects into the model, particle crushing and grading change are calculated for each load increment, in which the crushing probability of a particle during any loading increment is denoted as the corresponding increment of probability of the internal maximum shear stress exceeding its maximum shear strength. The model shows qualitative agreement with published experimental data. The effects of the model parameters, including initial porosity, particle strength, initial grading, and crushing mode, on the calculated results are discussed and compared with previous studies. Finally, the strengths and limitations of the model are discussed.     

加荷条件下软黏土的孔隙演化特征

开展上海软黏土的宏微观三轴剪切试验,研究软黏土受荷状态下孔隙的演化特征。结果表明：局部变形在加荷初期就开始发生。随着荷载的增加,细碎团聚体增多,孔隙不断地扩展,生成大的贯通孔隙,孔隙定向排列明显,剪切带形成。微观结构参数与剪应力比呈非线性正相关关系,最大孔隙面积、孔隙比、孔隙各向异性率及分布分维数在受荷初期缓慢地增大,后期快速增大。应变为8%时,最大各向异性率达到0.68,最大孔隙比为1.96。剪切带附近的微观结构参数都大于带外值。在受荷过程中,土的微观结构发生劣化,软黏土变形过程分为损伤开始、损伤发展剪切带形成和土体破坏3阶段,微观结构的劣化与土的宏观力学特性紧密相联系。