Diffuse instability of granular material under various drainage conditions: discrete element simulation and constitutive modeling

Acta Geotechnica - Diffuse instability is a typical failure mode of sand that occurs before the perfect plastic flow condition is attained. Whereas extensive laboratory experiments have...     

Numerical modeling of vertical drains with advanced constitutive models

The water flow into a vertical drain under an embankment loading is axisymmetric problem and therefore, the vertical drain system must be converted into equivalent plane strain model. The matching is achieved by manipulating the drain spacing and/or soil permeability according to relatively simple rules. This paper investigates the verification of matching approaches by comparing 2D plane strain and 3D unit cell results when complex constitutive models are used in the finite element analyses. The numerical results showed that the match was found to be satisfactory but not perfect. A full-scale plane strain analysis is subsequently applied to an embankment case history taken from Haarajoki, Finland, stabilized vertical drains and compared with field measurements.     

基于临界状态模型的砂土非共轴本构模拟

传统的砂土本构理论隐含了应力和塑性应变率的共轴条件,无法客观描述主应力轴旋转试验中的非共轴现象,并且当密度和围压变化较大时也不适用。基于材料状态相关砂土临界状态概念,将Pietruszczak和Stolle所提出的砂土本构模型进行了改进,并在模型中引入非共轴塑性流动理论来描述非共轴现象。通过对单剪试验和空心圆柱试验进行数值模拟,表明基于临界状态理论的非共轴模型能够合理描述主应力轴旋转过程中砂土的非共轴变形特性     

散粒材料压缩模量修正及群桩基础稳定性研究

天然沉积土在上覆土层重力作用下完成固结,其压缩模量大小和土层所受的前期固结压力大小直接相关。首先,分析岩土材料本构关系的主要影响因素,建立考虑模量随深度和体积应变变化的本构关系式;其次,建立桩基础稳定性问题的有限元求解格式,考虑水平荷载和下游冲刷深度对多种工况进行数值模拟分析;最后,根据计算结果,分析下游冲刷和水平荷载作用形成不对称接触边界对不同平面位置基桩受力特点,分析应力集中产生的原因及折屈失稳和整体稳定性问题。研究结果可为复杂大型工程群桩基础设计考虑桩、土及承台共同协调作用提供定量计算方法。     

Discrete element modeling of direct shear tests for a granular material

A succinct 3D discrete element model, with clumps to resemble the real shapes of granular materials, is developed. The quaternion method is introduced to transform the motion and force of a clump between local and global coordinates. The Hertz–Mindlin elastic contact force model, incorporated with the nonlinear normal viscous force and the Mohr–Coulomb friction law, is used to describe the interactions between particles. The proposed discrete element model is used to simulate direct shear tests of the irregular limestone rubbles. The simulation results of vertical displacements and shear stresses with a mixture of clumps are compared well with that of laboratory tests. The bulk friction coefficients are calculated and discussed under different contact friction coefficients and normal stresses. Copyright © 2009 John Wiley & Sons, Ltd.     

Competition mechanism between dilation and interlocking in granular soils: DEM simulation and constitutive modeling

Acta Geotechnica - Interlocking refers to a kind of resistance caused by the staggered arrangement of granular materials. In geotechnical engineering, it is considered as one of the important...     

基于颗粒组构特性的散体材料本构模型研究

通过散体介质材料单元颗粒排列组构表达的细观结构力学关系,建立了用颗粒密集度、颗粒排列组构关系和颗粒间摩擦特性等非连续介质材料特性参数描述的散体介质材料本构模型,从而实现散体介质材料宏观连续介质描述的等效应力表达.通过该模型可采用数值方法进行散体介质材料准静态情况下的力学特性分析.文中最后基于有限元软件ABAQUS,进行了该本构模型的二次开发.数值算例结果验证了所建立散体介质材料本构模型的适用性.     

Shear zones in granular material

Summary Shear Zones in Granular Materials. An Experimental Study of Their Structure and Mechanical GenesisA special ring-shear apparatus was designed to study in granular materials under continued shearing the development of shear zones and the accompanying changes in texture and stress state.Various series of experiments were run with densely packed, cohesionless materials in both dry and fluid-saturated states. For comparison, in a few tests also moderately cohesive materials were used. Materials and vertical load were chosen to either allow or suppress shear dilatancy, the latter case being characterised by severe grain crushing (cataclasis) in the shear zone proper. While growth and texture of dilating and non-dilating shear zones differ quite systematically, the build-up of stresses is quite similar in both cases, in particular with respect to the peak in shear stress.In many experiments stress measurements were carried out inside the granular pack, mainly by inserting small photoelastic cylinders, to establish the orientation of the maximum compressive stress in the vicinity of the shear band. The results leave little doubt that the shear bands produced between rigid platens are bounded by planes of maximum shear stress rather than by Coulomb-type slip planes. Inside a shear band, however, Coulomb slips are operative in deforming the softened shear zone material. This may be concluded from the regularly observed sets of oblique minor slips (Riedels) and discrete gliding planes.

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Zusammenfassung Scherzonen in körnigen Stoffen. Eine experimentelle Studie ihrer Strukturen und mechanischen EntstehungEin Ringschergerät wurde eigens entwickelt, um bei hinreichend langem Schervorgang die Entwicklung von Scherzonen in körnigem Material sowie die zugehörigen Struktur- und Spannungsänderungen studieren zu können.Verschiedene Versuchsreihen wurden mit dicht gepackten, nicht-kohäsiven Stoffen durchgeführt, sowohl in trockenem Zustand als auch gesättigt mit Flüssigkeit. Zum Vergleich wurde in einigen Versuchen auch mäßig verfestigtes, körniges Material verwendet. Geeignete Wahl von Material und vertikaler Belastung erlaubte es, Scherdilatanz zuzulassen oder zu unterdrücken; im letzteren Falle mit starker Kornzertrümmerung innerhalb der eigentlichen Scherzone (Bruchfließen). Während sich dilatierende und nicht dilatierende Scherzonen hinsichtlich Wachstum und Struktur systematisch unterschieden, war der Spannungsaufbau in beiden Fällen ähnlich. Dies gilt im besonderen für die Schubspannungsspitze (peak stress).In vielen Experimenten wurden Spannungsmessungen innerhalb der Körnerpackung ausgeführt, und zwar hauptsächlich mittels eingelegter photoelastischer Zylinderchen, um die Richtung der größten Druckspannung in Nähe der Scherzone zu ermitteln. Die Ergebnisse lassen wenig Zweifel, daß die zwischen starren Platten erzeugten Scherbänder von Ebenen größter Schubspannung begrenzt sind und nicht von Coulombschen Gleitebenen. Im Inneren der Scherbänder sind allerdings Coulombsche Gleitflächen an der Verformung des entfesteten Materials maßgeblich beteiligt, wie die regelmäßig wahrgenommenen, gestaffelten Sekundärgleitflächen (Riedel-Gleitflächen) und Gleitebenen zeigen.

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Résumé Zones de cisaillement en milieu granulaire. Etude expérimentale de leur structure et du mécanisme de genèseOn a conçu un dispositif annulaire spécial pour étudier le développement des zones de cisaillement en milieu granulaire, sous l'effet d'un effort de cisaillement continu ainsi que des modifications qui en résultent aussi bien dans la texture du milieu étudié que dans l'état de contrainte.Plusieurs séries d'expériences ont été effectuées sur un matériau fortement comprimé et denué de cohésion, tour à tour sec ou saturé de fluide. Dans un but de comparaison, on a aussi utilisé dans quelques cas, un matériau légèrement consolidé. Matériau et charge verticale furent choisis en sorte que l'effet de dilatation dû au cisaillement existe ou non: en l'absence de dilatation on a un important broyage des grains (cataclase) au sein de la zone de cisaillement. Alors que le développement et la texture des zones de cisaillement en dilatation ou sans dilatation présentent des différences systématiques, le développement des contraintes est très semblable dans les deux cas, en particulier en ce qui concerne la résistance au pic.Dans de nombreuses expériences, des mesures de contraintes furent faites à l'intérieur du milieu granulaire, par insertion de cylindres photoélastiques afin d'établir l'orientation de l'effort principal de compression, au voisinage de la zone de cisaillement. Les résultats laissent peu de doute sur le fait que la bande de cisaillement, entre les plaques rigides du dispositif est limitée par des plans de contrainte de cisaillement maximum et non par des plans de glissement du type des plans de Coulomb. Cependant, à l'intérieur d'une bande de cisaillement, des plans de glissement du type de Coulomb contribuent essentiellement à la deformation du matériau affaibli de la bande. On est amené à cette conclusion par l'observation systématique de familles de glissements obliques secondaires (Riedels) et de plans de glissements individualisés parallèles au cisaillement principal.

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With 33 Figures     

一类新型的散粒型土体本构理论

详细地介绍了国际上近30才发展起来的具有独特建模思想的一类新型的散粒型土体本构建模理论--亚塑性本构理论。将该理论与经典的弹塑性理论进行比较后发现,亚塑性理论的本构表达式自动隐含了弹塑性理论中相对应的一些基本概念和假定,无需额外引入,因此增加了模型的客观性。以Gudehus-Bauer亚塑性模型为例,分析了模型在临界状态时的本构特征。此外,通过三轴试验和循环剪切试验的亚塑性数值模拟表明,亚塑性本构模型能很好地反映无黏性散粒型土体的非弹性、非线性及剪胀（剪缩）性等主要应力-应变特性。     

The role of constitutive models in MPM simulations of granular column collapses

The granular column collapse is a well-established experiment which consists of having a vertical column of granular material on a flat surface and letting it collapse by gravity. Despite its simplicity in execution, the numerical modelling of a column collapse remains challenging. So far, much attention has been dedicated in assessing the ability of various numerical methods in modelling the large deformation and little to the role of the constitutive model on both the triggering mechanism and the flow behaviour. Furthermore, the influence of the initial density, and its associated dilatancy and strength characteristics, have never been included in the analyses. Most past numerical investigations had relied on simple constitutive relations which do not consider the softening behaviours. The aim of this study is to illustrate the influence of the constitutive model on the on-set of failure, the flow behaviour and the deposition profile using the material point method. Three constitutive models were used to simulate the collapse of two granular columns with different geometries and for two densities. The results of the simulations showed that the constitutive model had a twofold influence on the collapse behaviour. It defined the volume of the mobilised mass which spread along the flat surface and controlled the dissipation of its energy. The initial density was found to enhance the failure angle and flow behaviours and was more significant for small columns than for larger ones. The analysis of the potential energy of the mobilised mass explained the existence of two collapse regimes.     

砂土的流体动力学方程与本构模型的比较

目前砂土材料连续力学方程建模有两种途径,一种是源自于论证Navier-Stokes方程时所用的方法,称为流体动力学方法,主要针对普通固体、普通流体、超流、液晶、高聚物、颗粒物质等材料,它的基本做法是先给出守恒变量（如能量、动量、熵等）和对称破缺变量（如弹性应变、量子相位等）的一般运动方程,再用与具体材料有关的热力学函数和迁移系数来封闭它们;另一种方法是本构模型法,针对有塑性固体、非牛顿流体、砂土材料等材料,该做法特点是直接构建应力、应变、应力率、应变率、速度、密度、温度等变量之间的函数关系,并以此来封闭连续和牛顿方程。近年来采用这两种方法建立的砂土方程在文献上都有报道,因此,有必要对两者的特色、科学基础、适用范围,包括概念上的和具体方程等,进行比较,作为颗粒物理与土力学之间跨学科交流的一种尝试和沟通。通过比较得出,两种建模途径对表征砂土状态的完备变量集、屈服面、与塑性有关的耗散等使用了很不一样的思路和方程。     

ADINA有限元软件中材料本构的二次开发

美国ADINA R&D公司开发的软件产品ADINA经过20多年的商业开发,目前已成为全球最重要的非线性求解软件,尤其对结构非线性、流-固耦合等复杂问题的求解具有强大优势,被认为是非线性有限元发展方向的先导。然而,任何商业化的有限元软件都不可能满足客户的所有要求,例如,ADINA软件中没有岩土工程领域常用的Duncan-Chang模型。以土工数值分析中广泛应用的Duncan-Chang E-B模型为例,介绍在ADINA软件中进行材料本构二次开发的方法,给出了开发过程,通过对3个常规三轴压缩模型的数值模拟验证程序的可靠性。结果表明,基于ADINA开发的材料本构模型具有计算速度快、精度高和前后处理快捷方便的优点。另外,验证结果也表明该软件具有超强的非线性求解能力和可靠的求解结果。     

率相关本构模型的临界状态描述

临界状态是土的重要破坏特征,是当今许多土本构模型建立的基础。由于工程和试验中不能忽略时间因素,临界状态实际上是土在一定的时间作用下或者说一定的加载速率作用下表现出的破坏规律。率相关本构模型作为考虑了时间对土应力-应变关系影响的本构模型,理应可以描述临界状态。通过使用较为常用的率相关本构模型——过应力弹黏塑性模型对三轴不排水和排水剪切进行预测,探讨了这些模型对临界状态的描述情况。预测结果表明:(1)第1类过应力弹黏塑性模型(该模型认为屈服面是黏塑性体积应变率的等值面)计算所得的三轴不排水应力路径在临界状态线的下方出现应变软化,并且应力路径趋向于坐标原点,不能终止于临界状态;(2)第2类过应力弹黏塑性模型(认为屈服面是黏塑性标量因子的等值面)在对高应变率三轴排水剪切进行预测时,所得的最终应力比超过临界状态应力比;(3)第3类过应力弹黏塑性模型,亦即时间UH模型(认为屈服面是统一硬化参量变化率的等值面,并认为土产生应力塑性变形)在三轴不排水和排水剪切条件下均能较好反映临界状态。通过3种模型的公式分析了前述预测结果产生的原因。     

Discrete numerical modeling of particle transport in granular filters

Granular filters are an essential component in earth dams to protect the dam core from seepage erosion. This paper uses the particle flow method (PFM) to study the mechanism of particle transport in a base soil–filter system. The distributions of the eroded base-soil particles in different filters are traced and analyzed. The eroded mass and intruding depth of the eroded particles into the filters are obtained under different times and hydraulic gradients. The simulation results show that the eroded mass and intruding depth of the base-soil particles into the filter are related to the representative particle size ratio of the base soil to the filter, hydraulic gradient and erosion time. The numerical predictions are also compared with the empirical filter design criterion. The results show that the particle flow model provides an effective approach for studying the filtration micro-property and the erosion mechanism in a base soil–filter system, which is useful for filter design.     

Hydro-micromechanical modeling of wave propagation in saturated granular crystals

Biot theory predicts wave velocities in a saturated granular medium using the pore geometry, viscosity, densities, and elastic moduli of the solid skeleton and pore fluid, neglecting the interaction between constituent particles and local flow, which becomes essential as the wavelength decreases. Here, a hydro-micromechanical model, for direct numerical simulations of wave propagation in saturated granular media, is implemented by two-way coupling the lattice Boltzmann method (LBM) and the discrete element method (DEM), which resolve the pore-scale hydrodynamics and intergranular behavior, respectively. The coupling scheme is benchmarked with the terminal velocity of a single sphere settling in a fluid. In order to mimic a small amplitude pressure wave entering a saturated granular medium, an oscillating pressure boundary on the fluid is implemented and benchmarked with the one-dimensional wave equation. The effects of input waveforms and frequencies on the dispersion relations in 3D saturated poroelastic media are investigated with granular face-centered-cubic crystals. Finally, the pressure and shear wave velocities predicted by the numerical model at various effective confining pressures are found to be in excellent agreement with Biot analytical solutions, including his prediction for slow compressional waves.     

A state-dependent hyperelastic-plastic constitutive model considering shear-induced particle breakage in granular soils

Acta Geotechnica - An elastic–plastic constitutive model considering particle breakage for simulation of crushable granular soils behavior is proposed. In the model, elastic strain rates are...     

On the constitutive modeling of partially saturated interfaces

Generalization of soil–structure interface models from dry/saturated states to consider partially saturated states is studied in this paper. For this purpose, basic constitutive equations of a conventional elasto-plastic interface model are firstly presented. Then, consideration is given to the effect of partial saturation on definition of effective stress, location of the critical state line as well as the impact of interface state on plastic hardening modulus and dilatancy. For each concern, proper independent approaches together with associated constitutive equations are discussed to be included in the basic model as complementary ingredients. Among many different possibilities to combine complementary constitutive equations for effective stress, relocation of the critical state line with degree of saturation, and impact of the interface state on plastic hardening modulus and dilatancy, six essential cases are selected. Evaluations show that all six cases can realistically consider the impact of partial degree of saturation on the peak and residual shear strengths as well as the volume change behavior of unsaturated interfaces.     

模拟土体本构特性的热力学方法

简要介绍了建立岩土材料弹塑性本构模型的热力学方法。它不仅具有紧凑的数学结构,而且自动满足热力学定律,仅从两个热力学势函数,即自由能函数与耗散增量函数出发,就足以导出弹塑性理论必须的屈服条件,流动法则,硬化定律和弹性定律。通过理论证明指出,只要耗散增量函数依赖于当前应力,流动法则必然是非关联的,岩土材料的摩擦特性与非关联流动法则密不可分。介绍该方法在三维模型,岩土材料的微细观力学特性,应力应变的均匀化以及剪胀和各向异性方面应用的主要研究进展,并对一些重要的概念,诸如“储存的塑性功”,“Reynolds-Taylor状态”等,进行分析与解释。最后给出近期需进一步深入研究的几点建议。     

Particle shape evolution in natural carbonate granular wear material

A fundamental yet still unresolved puzzle provided by cataclasis is whether particle size reduction mostly progresses through time by the same fragmentation mechanism or not. Available field, laboratory and numerical modelling results on the evolution of cataclastic rocks are still controversial. The evidence that cataclastic rocks exert a primary control on the frictional strength, stability, seismic velocity and permeability properties of fault zones encourages further research on cataclasis. Here, we report data on particle shape from natural cataclastic rocks in poorly layered carbonates in the Apulian foreland of the Southern Apennines of Italy. Particle shape analyses show that particle angularity decreases with increasing size and, for a given size class, it decreases with increasing fractal dimension of the particle size distribution. These results offer support to the temporally and spatially variable nature of rock comminution.