Non‐coaxiality and stress–dilatancy rule in granular materials: FE investigation within micro‐polar hypoplasticity

This paper deals with FE investigations of shear localization in dilatant granular bodies. The calculations were carried out with a hypoplastic constitutive law enhanced by micro‐polar terms to properly model the shear zone evolution. The behaviour of an initially medium dense sand specimen with very smooth and very rough horizontal boundaries was analyzed during a plane strain compression test. A stochastic distribution of the initial void ratio was assumed to be spatially correlated. Attention was focused on the non‐coaxiality of the directions of the principal strain increments and principal stresses in the shear zone and on the stress–dilatancy rule. Copyright © 2008 John Wiley & Sons, Ltd.     

Effect of grain crushing on shear localization in granular bodies during plane strain compression

This article deals with the effect of grain crushing on shear localization in granular materials during plane strain monotonic compression tests under constant lateral pressure. The grain diameter and the initial void ratio were stochastically distributed using a spatial correlation. To describe the mechanical behavior of cohesionless granular materials during a monotonic deformation path in plane strain compression, we used a micropolar hypoplastic constitutive model that is able to describe the salient properties of granular bodies including shear localization. The model was extended by introducing changes to the grain diameter with varying pressure using formulae from breakage mechanics proposed for crushable granulates. The initial void ratios and grain diameters took the form of correlated random spatial fields described by both symmetric and nonsymmetric random distributions using a homogeneous correlation function. The field realizations were generated with the help of an original conditional rejection method. A few representative samples of the random fields selected from the generated set were taken into account in numerical calculations. Copyright © 2011 John Wiley & Sons, Ltd.     

Influence of initial density of cohesionless soil on evolution of passive earth pressure

This paper focuses on the influence of the initial void ratio on the evolution of the passive earth pressure and the formation of shear zones in a dry sand body behind a retaining wall. For the numerical simulation a rigid and very rough retaining wall undergoing a horizontal translation against the backfill is considered. The essential mechanical properties of cohesionless granular soil are described with a micro-polar hypoplastic model which takes into account stresses and couple stresses, pressure dependent limit void ratios and the mean grain size as a characteristic length. Numerical investigations are carried out with an initially medium dense and initially loose sand using a homogeneous and random distribution of the initial void ratio. The geometry of calculated shear zones is discussed and compared with a corresponding laboratory model test.     

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.     

DEM simulation of collapse behaviours of unsaturated granular materials under general stress states

In this study, a numerical simulation of true triaxial tests was conducted using the three-dimensional distinct element method (DEM) in order to examine how unsaturated granular materials collapse under general stress states. The collapse process was simulated by reducing the intergranular adhesive forces corresponding to the effect of the capillary suction during the isotropic compression and the shearing processes under general stress states. Based on the relationship between the void ratio and the mean principal stress after collapsing, it was found that the initially soaked compression line obtained with an inundation test may be used to predict the collapse of granular materials under a general stress state. From the analysis for the fabric tensor in the particle aggregate after collapsing, the skeleton structures became identical to those in which no intergranular adhesive force was applied. Furthermore, even though the collapse process was simulated under a plane strain condition, the shear band inside the sample did not occur clearly, and the slippage between particles was instead induced randomly during collapsing.     

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.     

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.     

Numerical simulation of the effect of interface friction of a bounding structure on shear deformation in a granular soil

Recently, the shear behavior of a cohesionless granular strip that is in contact with a very rough surface of a moving bounding structure has been numerically investigated by several authors by using a micropolar hypoplastic continuum model. It was shown that the micropolar boundary conditions assumed along the interface have a strong influence on the deformations within the granular layer. In previous investigations, only interface friction angles for very rough bounding structures were assumed. In contrast, the focus of the present paper is on the influence of the interface roughness on the deformation behavior of the granular strip when the interface friction angle is lower than the peak friction angle of the granular material. In addition to the interface friction angle, particular attention is also paid to the influence of the mean grain diameter, the solid hardness, the initial void ratio, and the vertical stress on the maximum horizontal shear displacement within the granular layer before sliding is started. Copyright © 2011 John Wiley & Sons, Ltd.     

无黏性土压缩模型及其验证

土体本构模型的建立往往需要以等向压缩模型为基础。通过对无黏性土等向压缩特性的分析,发现无黏性土等向压缩状态下压缩指数的大小与当前孔隙比和球应力密切相关,进而提出了以当前孔隙比和球应力为变量的可分离函数表示的压缩指数表达式。在此基础上得到一个可以描述无黏性土压缩特性的三参数压缩模型。与试验数据的对比表明,该模型能够较好地拟合不同初始孔隙比下无黏性土等向压缩试验的孔隙比-应力关系。与以极限压缩曲线为参考线建立的压缩模型相比,在拟合低应力区无黏性土的孔隙比-应力关系时,提出的新模型更具有实用性。新模型也可为无黏性土建立本构模型提供基础。     

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.     

Evaluation of Shear Modulus and Damping Ratio of Granular Materials Using Discrete Element Approach

In this paper, an attempt has been made to highlight the influence of different parameters such as number of cycles, confining pressure, void ratio, gradation, initial anisotropy and stress path on the dynamic properties of granular materials using Discrete Element Method (DEM). A series of strain controlled cyclic triaxial numerical simulations using three dimensional DEM have been carried out on an assembly of spheres. Dynamic properties such shear modulus (G) and damping ratio (D) were determined from the typical hysteresis loop obtained during cyclic triaxial test simulation. It has been observed from the test results that the numerical simulation using DEM has captured the variation of dynamic properties over a wide range of shear strain values for different parameters considered for the current investigation. Maximum shear modulus (G _max) was found to be influenced by initial confining pressure, void ratio, gradation and initial anisotropy. Whereas, the damping ratio (D) was found to be influenced by number of cycles, initial confining pressure, gradation and stress path. Further it has been shown that the variation of shear modulus with shear strain can be divided into three distinct zones such as Isotropic Zone (IZ), Anisotropic Zone (AZ) and Stable Anisotropic Zone (SAZ). A drastic reduction of shear modulus with shear strain has been observed in the Anisotropic Zone (AZ). In addition, the results obtained using numerical simulations have been compared with the laboratory experimental values.     

Discrete simulations of a triaxial compression test for sand by DEM

A quasi‐static homogeneous drained triaxial compression test on cohesionless sand under constant lateral pressure was simulated using a three‐dimensional discrete element method. Grains were modelled by means of particle clusters composed of rigid spheres or spheres with contact moments imitating irregular particle shapes. Attention was paid to the effect of initial void ratio and grain shape mixture on the shear strength, volume changes, force chains, kinetic, elastic and dissipated energies. In addition, the effect of the mean grain size, grain size distribution, grain size range, specimen size and roughness and stiffness of boundaries was numerically analysed in initially dense sand. Some numerical results were compared with available experimental results. Copyright © 2014 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.     

Coupling pore-water pressure with distinct element method and steady state strengths in numerical triaxial compression tests under undrained conditions

The undrained shear behaviour of sands has been a key topic after the devastating geo-disasters during the 1964 Niigata Earthquake in Japan. Extensive geo-technical soil tests, especially undrained triaxial compression tests, have revealed that the liquefaction phenomenon was the major cause for the disaster expansions. To numerically reproduce the liquefaction phenomenon, the pore-water pressure was coupled with a distinct element method. In this model, the dynamic changes in pore-water pressure were taken into consideration by the changes in volumetric strain and modulus of compressibility of water in the respective measurement spheres. Fluid-flows among the measurement spheres were controlled by Darcy’s law. The effective stress paths and steady state strengths in undrained triaxial compression tests associated with the wide ranges of initial void ratio were investigated. The effective mean stresses of medium-dense to dense numerical specimens at the steady state were negatively proportional to the initial void ratio. Loose numerical specimens reproduced quasi-liquefaction with the effective mean stresses that were less than 25% of the initial value. The medium-dense numerical specimens reproduced the phase transformation that was a typical characteristic of granular materials. The rolling restraints did not much influence of the effective angle of internal friction but strongly affected pore-water pressure behaviour within a certain range of initial void ratio.     

DEM study of fabric features governing undrained post-liquefaction shear deformation of sand

In an effort to study undrained post-liquefaction shear deformation of sand, the discrete element method (DEM) is adopted to conduct undrained cyclic biaxial compression simulations on granular assemblies consisting of 2D circular particles. The simulations are able to successfully reproduce the generation and eventual saturation of shear strain through the series of liquefaction states that the material experiences during cyclic loading after the initial liquefaction. DEM simulations with different deviatoric stress amplitudes and initial mean effective stresses on samples with different void ratios and loading histories are carried out to investigate the relationship between various mechanics- or fabric-related variables and post-liquefaction shear strain development. It is found that well-known metrics such as deviatoric stress amplitude, initial mean effective stress, void ratio, contact normal fabric anisotropy intensity, and coordination number, are not adequately correlated to the observed shear strain development and, therefore, could not possibly be used for its prediction. A new fabric entity, namely the Mean Neighboring Particle Distance (MNPD), is introduced to reflect the space arrangement of particles. It is found that the MNPD has an extremely strong and definitive relationship with the post-liquefaction shear strain development, showing MNPD’s potential role as a parameter governing post-liquefaction behavior of sand.     

Concept of critical void ratio used in estimating dynamic stability of sands

Some authors use the concept of critical void ratio of sands to describe sand behavior under dynamic load. This paper presents a new procedure of experimental determination of the critical void ratio of sands under consolidated undrained triaxial compression. At present, there is no technical possibility for determining the critical void ratio of sand under dynamic loads, particularly in shear zones. The mechanism of dynamic load is such that both pore pressure and effective stresses (indirect indicators of the change in the void ratio of sand under undrained conditions) change several times, even during one cycle. It is established that, because of dynamic loading, saturated sands of any density tend to the state of zero dynamic dilatancy when shear zones of constant thickness form in sands, where further strain accumulation is localized. The investigation into the state of zero dynamic dilatancy is fundamentally important for the estimation of the dynamic stability of sands.     

FE-modeling of shear resistance degradation in granular materials during cyclic shearing under CNS condition

The behaviour of dry and cohesionless granular material during quasi-static cyclic shearing under a constant normal stiffness (CNS) condition is theoretically studied. A particular attention is laid to the volumetric strain change and the degradation of the shear resistance in the course of shearing. Numerical calculations are carried out for several shear cycles under boundary conditions which are relevant to investigate the shear interface behaviour. The global and local evolution of deformation, stress and density within the granular material is investigated with a finite element method on the basis of a hypoplastic constitutive model extended by micro-polar quantities: rotations, curvatures and couple stresses. A mean grain diameter is used as a characteristic length of micro-structure. The constitutive equations for stresses and couple stresses take also into account the effect of the evolution of the void ratio, pressure dependent relative density, direction of rate of deformation and rate of curvature. The numerical results are qualitatively compared with corresponding laboratory tests on direct wall shearing performed by DeJong, Randloph and White. In addition, the results for cyclic shearing of an infinite granular layer between two very rough boundaries under CNS conditions are also enclosed and discussed.     

An Anisotropic Model for Granular Material Based on Experiments

Soil is a heterogeneous material and most natural soil deposits show a definite stratification. The mechanical behaviour of such material is generally different in different directions, especially in the direction parallel and perpendicular to the stratification. A series of isotropic compression tests were carried out to study the behavior of granular material produced under controlled stratification in the laboratory. These tests were conducted both on cylindrical and square prismatic tri-axial specimens. It was observed that for hydrostatic loading, the strain response was different in different directions, especially in directions parallel and perpendicular to the direction of soil deposition. A definite trend of anisotropy was observed in the deformation pattern. The observed anisotropy is modeled in this paper by treating soil-dilatancy as a variable quantity. The equation of the plastic potential surface of the model which obeys a non-associated flow rule, is assumed to be dependent on three main variables confining pressure (\(\sigma_{3}\)), void ratio (e) and the angle of bedding plane orientation (δ) during deposition. The angle of bedding plane orientation (δ) was measured with respect to the direction of the major principal stress. The model has a cap yield surface in the isotropic stress direction, which is supplemented by a shear hardening Mohr–Coulomb surface in the deviator direction. This paper focuses on predicting the anisotropic strain response of stratified soil deposits subjected to isotropic compression. The proposed anisotropic model incorporates within an existing strain-hardening sand model, a modified cap yield surface and a modified plastic potential function related to the cap surface, to account for the anistropic response observed in isotropic compression tests. The two dimensional stress–strain model was extended to three dimensional Cartesian space. The strain anisotropy observed in the isotropic compression tests was predicted by the three dimensional anisotropic model proposed for granular materials.     

颗粒材料剪胀性的微观力学分析

剪胀性是颗粒材料在加载过程中表现出来的重要变形特性。以孔隙胞元描述颗粒材料内部结构的最小单元,通过对单个孔隙胞元进行剪切受力分析,探讨了剪切过程中颗粒材料体积的改变对应力比和单个孔隙胞元形状的依赖关系,解释了排列密实的颗粒材料在剪切过程中先压缩后剪胀的微观机制。用离散元数值模拟得到了在双轴剪切过程中单个孔隙胞元形状以及孔隙胞元体积变形的演化过程。离散元数值结果表明,加载过程中孔隙胞元形状由初始各向同性到沿大主应力方向变大变长、体积变形先压缩后膨胀,并且体积变形在加载过程中存在局部化现象,体积变化大的孔隙胞元在较大变形时,排列成倾斜的窄带。综合孔隙胞元的受力分析和离散元数值结果表明,致密排列颗粒材料的剪胀性与微观尺度上孔隙胞元的几何结构及其内部的力链传递方式密切相关。