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.     

Numerical investigations of shear localization in a micro‐polar hypoplastic material

In this paper a micro‐polar continuum approach is proposed to model the essential properties of cohesionless granular materials like sand. The model takes into account the influence of particle rotations, the mean grain size, the void ratio, the stresses and couple stresses. The constitutive equations for the stresses and couple stresses are incrementally non‐linear and based on the concept of hypoplasticity. For plane strain problems the implementation of the model in a finite element program is described. Numerical studies of the evolution of micro‐polar effects within a granular strip under plane shearing are presented. It is shown that the location and evolution of shear localization is strongly influenced by the initial state and the micro‐polar boundary conditions. For large shearing the state quantities tend towards a stationary state for which a certain coupling between the norm of the stress deviator and the norm of the couple stress tensor can be derived. Copyright © 2003 John Wiley & Sons, Ltd.     

Shearing of a narrow granular layer with polar quantities

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.     

A comparative study of the hypoplasticity and the fabric‐dependent dilatant double shearing models for granular materials

In this paper, we consider the mechanical response of granular materials and compare the predictions of a hypoplastic model with that of a recently developed dilatant double shearing model which includes the effects of fabric. We implement the constitutive relations of the dilatant double shearing model and the hypoplastic model in the finite element program ABACUS/Explicit and compare their predictions in the triaxial compression and cyclic shear loading tests. Although the origins and the constitutive relations of the double shearing model and the hypoplastic model are quite different, we find that both models are capable of capturing typical behaviours of granular materials. This is significant because while hypoplasticity is phenomenological in nature, the double shearing model is based on a kinematic hypothesis and microstructural considerations, and can easily be calibrated through standard tests. Copyright © 2006 John Wiley & Sons, Ltd.     

Modelling strain localization in granular materials using micropolar theory: mathematical formulations

It has been known that classical continuum mechanics laws fail to describe strain localization in granular materials due to the mathematical ill‐posedness and mesh dependency. Therefore, a non‐local theory with internal length scales is needed to overcome such problems. The micropolar and high‐order gradient theories can be considered as good examples to characterize the strain localization in granular materials. The fact that internal length scales are needed requires micromechanical models or laws; however, the classical constitutive models can be enhanced through the stress invariants to incorporate the Micropolar effects. In this paper, Lade's single hardening model is enhanced to account for the couple stress and Cosserat rotation and the internal length scales are incorporated accordingly. The enhanced Lade's model and its material properties are discussed in detail; then the finite element formulations in the Updated Lagrangian Frame (UL) are used. The finite element formulations were implemented into a user element subroutine for ABAQUS (UEL) and the solution method is discussed in the companion paper. The model was found to predict the strain localization in granular materials with low dependency on the finite element mesh size. The shear band was found to reflect on a certain angle when it hit a rigid boundary. Applications for the model on plane strain specimens tested in the laboratory are discussed in the companion paper. Copyright © 2006 John Wiley & Sons, Ltd.     

FE-studies on the influence of initial void ratio,pressure level and mean grain diameter on shear localization

The paper is concerned with shear localization in the form of a spontaneous shear zone inside a granular material during a plane strain compression test. The influence of an initial void ratio, pressure and a mean grain diameter on the thickness of a shear zone is investigated. A plane strain compression test with dry sand is numerically modelled with a finite element method taking into account a polar hypoplastic constitutive relation which was laid down within a polar (Cosserat) continuum. The relation was obtained through an extension of a non-polar hypoplastic constitutive law according to Gudehus and Bauer by polar quantities: rotations, curvatures, couple stresses and a characteristic length. It can reproduce the essential features of granular bodies during shear localization. The material constants can be easily calibrated. The FE-calculations demonstrate an increase in the thickness of the shear zone with increasing initial void ratio, pressure level and mean grain diameter. Polar effects manifested by the appearance of grain rotations and couple stresses are only significant in the shear zone. A comparison between numerical calculations and experimental results shows a satisfying agreement. Copyright © 1999 John Wiley & Sons, Ltd.     

含细粒砂土反常剪切行为的数值模拟研究

针对含细颗粒砂土的反常剪切行为,开展了双轴剪切试验的数值模拟,从宏细观角度分析了其反常剪切行为发生的内在机制。数值模拟结果表明,增加围压能提高含细颗粒砂土的抗剪切液化能力,该反常行为的根本原因在于围压上升使得粗细颗粒更有效地参与了力链传递,增加了颗粒间的接触,增强了土体的密实度。细颗粒在土骨架中的移动对砂土的液化起着至关重要的作用,而粗颗粒仅起次要作用。研究表明,细颗粒在剪切过程中会持续从有效土骨架中移出成为无效颗粒,而部分粗颗粒也因失去细颗粒的支撑作用会脱离土骨架,直至试样最终液化。细颗粒一般参与土骨架中的弱力链,而粗颗粒则一般参与强力链,导致细颗粒较粗颗粒更容易在土骨架中移动。     

基于CLoE与Gudehus-Bauer亚塑性模型的颗粒材料应变局部化对比研究

基于CLoE与Gudehus-Bauer亚塑性模型数值模拟了平面应变条件下Hostun砂的应变局部化现象。从侧向压力和初始缺陷两个方面对比研究了两种模型所预测应变局部化的产生及演化模式。结果表明：（1）两种模型均能反映Hostun砂刚度随着侧向压力提高而增大的现象。（2）相比Gudehus-Bauer亚塑性模型,CLoE亚塑性模型所得出的应变局部化形态与试验结果更加一致。（3）CLoE亚塑性模型能够反映随着荷载增加,砂的体积先膨胀后缩小的特点。（4）相比Gudehus-Bauer亚塑性模型,CLoE亚塑性模型所得到的应变-应力曲线能够更明显地反映应变局部化带中单元的软化现象。（5）CLoE亚塑性模型能够更好地模拟由初始缺陷导致的不均匀应变。总的来说,所得的数值结果表明,CLoE亚塑性模型能够较好地模拟侧向压力和初始缺陷对应变局部化的影响,在模拟应变局部化现象方面较Gudehus-Bauer更有优势。然而,现有CLoE亚塑性模型无法考虑孔隙比,也未包含颗粒材料内尺度变量,有待进一步完善。     

Diffuse bifurcations engraving diverse shear bands in granular materials

Shear bands with characteristic spatial patterns observed in an experiment for a cubic or parallelepiped specimen of dry dense sand were simulated by numerical bifurcation analysis using the Cam‐clay plasticity model. By incorporating the subloading surface concept into the plasticity model, the model became capable of reproducing hardening/softening and contractive/dilative behavior observed in the experiment. The model was reformulated to be compatible with the multiplicative hyperelasto‐plasticity for finite strains. This enhanced constitutive model was implemented into a finite‐element code reinforced by a stress updating algorithm based on the return‐mapping scheme, and by an efficient numerical procedure to compute critical eigenvectors of elastoplastic tangent stiffness matrix at bifurcation points. The emergence of diamond‐ and column‐like diffuse bifurcation modes breaking uniformity of the materials, followed by the evolution of shear bands through strain localization, was observed in the analysis. In the bifurcation analysis of plane strain compression test, unexpected bifurcation modes, which broke out‐of‐plane uniformity and led to 3‐dimensional diamond‐like patterns, were detected. Diffuse bifurcations, which were difficult to observe by experiments, have thus been found as a catalyst creating diverse shear band patterns.     

初始静剪应力对粗粒土与结构接触面循环力学特性的影响

运用80 t大型三维接触面试验机,对初始静剪应力存在时粗粒土与结构接触面循环力学特性及初始静剪应力大小的影响进行了研究。循环剪切时,接触面沿初始静剪应力方向产生了明显的切向位移,且该位移与正交切向的剪切路程基本呈直线关系,该直线与初始静剪应力的夹角和初始静剪应力水平关系可用二次多项式描述。初始静剪应力大小对接触面抗剪强度、正交切向应力-应变关系形式影响较小,主要影响正交切向应力峰值、接触面剪切体变数值及剪切体变与切向位移关系等。初始静剪应力越大,该方向产生的切向位移越大,其正交切向应力峰值越小,该应力峰值对应的切向位移亦越小,接触面剪切硬化程度越高;初始剪切时接触面剪胀量越大,而后期循环剪切时剪缩量和剪胀量则越小。     

散粒体材料间接触面力学特性的单剪试验研究

在清华大学土与结构接触面循环加载剪切试验机的基础上, 研制了可进行两种散粒体间接触面试验的叠环式单剪试验系统,并对糯扎渡高心墙堆石坝坝料的接触特性进行了系统的试验研究。结果表明,两种散粒体材料间接触面的强度包线为其单相材料强度下的包线。当达到破坏强度后,在接触界面附近会产生集中的“刚塑性”接触面剪切变形,其位置发生在强度最薄弱处。两种散粒体间的接触变形特性可通过刚塑性模型来描述。     

Deterministic and statistical size effect during shearing of granular layer within a micro‐polar hypoplasticity

The paper deals with numerical investigations of a deterministic and statistical size effect in granular bodies during quasi‐static shearing of an infinite layer under plane strain conditions, free dilatancy and constant pressure. For a simulation of the mechanical behaviour of a cohesionless granular material during a monotonous deformation path, a micro‐polar hypoplastic constitutive relation was used which takes into account particle rotations, curvatures, non‐symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The proposed model captures the essential mechanical features of granular bodies in a wide range of densities and pressures with a single set of constants. In the paper, a deterministic and statistical size effect is analysed. The deterministic calculations were carried out with an uniform distribution of the initial void ratio for four different heights of the granular layer: 5, 50, 500 and 2000 mm. To investigate the statistical size effect, the Monte Carlo method was applied. The random distribution of the initial void ratio was assumed to be spatially correlated. Truncated Gaussian random fields were generated in a granular layer using an original conditional rejection method. The sufficient number of samples was determined by analysing the convergence of the outcomes. In order to reduce the number of realizations without losing the accuracy of the calculations, stratified and Latin hypercube methods were applied. A parametric analysis of these methods was also presented. Some general conclusions were formulated. Copyright © 2007 John Wiley & Sons, Ltd.     

超固结粘土的剪切带数值模拟

基于中井的子负荷面本构关系模型,采用高精度的隐式应力积分算法,研究了平面应变试验中超固结粘土试样的变形局部化问题。模拟了不同的加载速度和边界约束条件,得到了超固结比为8的藤森粘土土体内部明显可见的X型剪切带和单一型剪切带。结果表明：土体的剪胀特性、孔隙水在土体内的移动规律以及边界约束条件对剪切带的形成和发展起着控制作用。     

土工格栅与土界面作用特性试验研究

土工格栅与土的界面摩擦特性指标是加筋土工程设计的关键。通过分析土工格栅与土的界面摩擦作用和进行了直剪摩擦试验和拉拔摩擦试验,测试了两种试验条件的界面摩擦特性。在两种试验条件下,土工格栅加筋土复合体的抗剪强度均有界面摩擦角φsq和界面凝聚力csq,且土工格栅与土相对位移量的不同,其复合体的强度机理有区别。在拉拔摩擦试验中,剪应力峰值强度对应的剪切变形值高于直剪摩擦试验中剪应力峰值强度的剪切变形值5～10倍以上。两种试验均有其适用性,而土与土工格栅的相对位移较小时直剪摩擦试验较能反映实际;土与土工格栅相对位移较大时土与格栅双面均发生相对位移,拉拔摩擦试验更为合适。随法向应力的增大,直剪摩擦和拉拔摩擦试验的剪应力峰值以及剪应力峰值对应的位移均提高。直剪摩擦的剪切速度小,剪应力峰值强度高,且达到峰值强度的剪切位移大;增加剪切速度,剪应力峰值强度降低,且对应的位移也减少,其原因是界面上的孔隙水压力消散和筋材的应力松弛。应根据具体工程的需要选择直剪摩擦试验和拉拔摩擦试验确定设计参数。     

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.     

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。     

粗粒土与结构接触面特性的离散-连续耦合数值研究

三维变形体离散元法能够自动检索接触关系,并对具有不规则形状的粗粒土颗粒和结构物进行有限差分网格离散,因此,具有模拟离散-连续耦合问题的先天优势。采用随机模拟技术生成粗粒土三维数值试样,基于变形体离散元进行粗粒土与结构接触面特性的数值试验,研究了不同接触面粗糙程度的接触面力学特性,对比了粗粒土与结构物在单剪和直剪状态下的接触面力学特性,从宏观和细观两个层面分析了数值试验结果。结果表明,数值试验能较好地反映粗粒土与结构接触面的力学特性,其剪应力-相对剪切位移曲线与试验结果规律相似;接触面粗糙程度对接触面的强度和变形特性影响较大,其机制在于剪切对试样的扰动程度不同;直剪和单剪状态下试样剪应力-相对剪切位移均为双曲线,单剪试验的初始剪切刚度低于直剪试验,两种试验得到接触面抗剪强度指标比较接近。     

基于图像相关分析的土体剪切带识别方法

提出了一种基于数字照相量测和图像相关性分析技术的土体剪切带识别方法。首先,在模型试验中,用数码相机采集土体全程变形图像序列;接着,在图像全局观测范围内粗略搜索到剪切带发生的大致区域;然后,布置跨越剪切区域的多对测点线,进行局部范围精密搜索,识别出剪切带的准确位置与形状, 并确定剪切带的边界点。与在模型上描画网格线等传统方法相比,该法操作简单,量测准确,适用于模型试验中岩土材料的剪切带识别及其厚度、倾角、带内变形和演变过程等特性的试验研究;最后,给出了一个大型砂土剪切试验中的应用实例。结果表明,基于图像相关分析的识别土体剪切带的方法是可行而有效的。     

土与结构界面位移特性静动力单剪试验研究

土与结构接触面是工程中经常遇到的,剪切试验是研究界面特性的主要方法之一。单剪试验既可以研究界面的特性,又可以考虑土体受力变形的实际特征,土体变形和界面错动位移的关系是尚未被注意的问题。通过淤泥质粉质黏土的静、动力单剪试验和进行不同法向应力、不同剪切应力幅值的对比试验,得到界面位移与循环周数、土体应变的试验曲线。结果表明,静力单剪试验的初期剪应力迅速增大,其后增长速率逐渐减小,没有出现软化现象;在剪切初期,主要是土体发生剪切位移,达到一定位移量后,土体和钢板之间开始出现较为明显的滑移;在一定的土体应变范围内静力单剪界面错动位移和土体应变有近似线性关系;动力单剪的界面错动位移和土体应变有很好的线性关系;静动力试验界面位移与土体应变关系线的斜率总体上静力试验结果高于动力试验值,线性关系的斜率变化范围不大