Statistical analysis of stress transmission in wet granular materials

The micromechanics of wet granular materials encompasses complex microstructural and capillary interconnects that can be readily described through a formal derivation of stress transmission in such a 3‐phase medium. In the quest for defining an appropriate stress measure, the stress tensor expression that results from homogenization [Duriez et al. J Mech Phys Solids 99 (2017): 495‐511] of such a medium provides theoretical insights necessary to extract useful information on the relationship between capillary effects and microforce interactions via several small‐scale parameters whose evaluation can be challenging. Using instead a statistical approach where microvariable distributions are described by probability density functions, the current study provides simple estimates of stress components in terms of only a few tractable microvariables such as coordination number and fabric anisotropy. In particular, the latter recognizes details of contacts such as force interactions being either mechanical or capillary, including interactions with and without mechanical contact. The developed expressions are in a good agreement with discrete element method simulation results of the triaxial loading of a wet granular assembly, notably for hydrostatic (mean) pressure. A new set of dimensionless groups is also identified to characterize the significance of mechanical and capillary physics, which facilitates a better understanding of the contribution of dominating elements to stress, while also providing the opportunity to incorporate important capillary effects in micromechanically based constitutive formulations.     

Revisiting the existence of an effective stress for wet granular soils with micromechanics

A possible effective stress variable for wet granular materials is numerically investigated based on an adapted discrete element method (DEM) model for an ideal three‐phase system. The DEM simulations consider granular materials made of nearly monodisperse spherical particles, in the pendular regime with the pore fluid mixture consisting of distinct water menisci bridging particle pairs. The contact force‐related stress contribution to the total stresses is isolated and tested as the effective stress candidate for dense or loose systems. It is first recalled that this contact stress tensor is indeed an adequate effective stress that describes stress limit states of wet samples with the same Mohr‐Coulomb criterion associated with their dry counterparts. As for constitutive relationships, it is demonstrated that the contact stress tensor used in conjunction with dry constitutive relations does describe the strains of wet samples during an initial strain regime but not beyond. Outside this so‐called quasi‐static strain regime, whose extent is much greater for dense than loose materials, dramatic changes in the contact network prevent macroscale contact stress‐strain relationships to apply in the same manner to dry and unsaturated conditions. The presented numerical results also reveal unexpected constitutive bifurcations for the loose material, related to stick‐slip macrobehavior.     

3D DEM simulation of principal stress rotation in different planes of cross-anisotropic granular materials

Three-dimensional Discrete Element Method simulations have been performed to study the deformation of cross-anisotropic granular materials under principal stress rotation (PSR), for rotation planes oriented at different angles θ with respect to the bedding plane. The simulations have been conducted with a novel technique for applying specified stresses at three-dimensional boundaries. The results are qualitatively in agreement with experimental results from literature. Cumulative volume contraction is always observed under continuous PSR and increases with increasing θ. The dilatancy rate decreases with increasing number of PSR cycles, tending to zero. The noncoaxiality angle between the strain increment and the stress in the PSR plane increases with increasing number of cycles, reaching the same asymptotic value for samples of various densities and for various θ. Periodic oscillations of the dilatancy rate and noncoaxiality angle within each PSR cycle are observed with an increasing oscillation magnitude with increasing θ, due to the larger fabric anisotropy within the PSR plane. When θ = 30 or 60°, significant noncoaxial strain accumulation occurs in the plane perpendicular to the PSR plane due to the oblique angle between the PSR plane and the bedding plane, echoing the major principal fabric direction's being neither parallel nor perpendicular to the PSR plane. The macroscopic behavior of the samples is related to the microscopic parameters including coordination number and fabric anisotropy. With increasing number of cycles, the difference between normalized stress/strain/fabric increment tensors tends to become constant, with only a small lag between each pair, irrespective of θ.     

Influence of liquid bridges on the mechanical behaviour of polydisperse granular materials

We investigate a polydisperse granular material in which the particle interactions are governed by a capillary force law. The cohesion force for a grain‐pair with unequal diameters is expressed as an explicit function of the inter‐particle distance and the volume of the liquid bridge. This analytical relation is validated by experiments on a reference material. Then, it is completed by a rupture criterion and cast in the form of a force law that accounts for solid contact, capillary force and rupture characteristics of a grain‐pair. Finally, in order to evaluate the influence of capillary cohesion on the macroscopic behaviour, radial and axial compression tests on cylindrical assemblies of wet particles are simulated using a 3D distinct element method. Copyright © 2005 John Wiley & Sons, Ltd.     

A micromorphic elastoplastic model and finite element simulation on failure behaviors of granular materials

One of the purposes in this study is to develop a modified micromorphic continuum model for granular materials on the basis of a micromechanics approach. A symmetric curvature tensor is proposed in this model, and a symmetric couple stress tensor is derived conjugating the symmetric curvature tensor. In addition, a correct derivation is presented to obtain the symmetric stress tensor conjugated with the symmetric strain tensor. The modified model provides a complete deformation mode for granular materials by considering the decomposition for motions (displacement and rotation) of particles. Consequently, the macroscopic constitutive relationships and constitutive moduli are derived in expressions of the microstructural information. Furthermore, the balance equations and boundary conditions are obtained for the modified micromorphic model. By considering the extended Drucker-Prager yield criterion, the micromorphic elastoplastic model is developed. Another purpose of this study is to derive the finite element formulation for the developed micromorphic elastoplastic model. Based on the ABAQUS user element (UEL) interface, numerical simulations investigated the load-displacement relationship and the strain localization behavior of granular materials and investigated the influence of microscopic parameters in the micromorphic model on these macroscopic mechanical responses. Numerical results illustrate the presented model's capability of simulating the strain-softening and strain localization behaviors, and the capability of considering the influence of microstructural information on the macroscopic mechanical behaviors of granular materials.     

Second‐order work analysis for granular materials using a multiscale approach

It has been established that the second‐order work criterion is a general necessary condition for all instabilities by divergence in rate‐independent granular materials. The relation between the values of discrete second‐order work at the intergranular contact point level and its global macroscopic value is recalled at the beginning of this paper. Then, the basic purpose of the paper is tackled by an analysis of the main features of second‐order work criterion in relation with the granular microstructure. For that, it is considered a novel micromechanical model (the so‐called ‘H‐microdirectional model’), which has the property to involve three scales: grain scale, mesoscale with a specific granular configuration and continuum mechanics macroscale. Eventually, these exhibited features (a bifurcation stress domain and some instability cones) are qualitatively compared with the ones provided by direct numerical simulations issued from a discrete element model. The ultimate goal is to analyse what happens at the granular scale, when the macrosecond‐order work is vanishing at the macrolevel. Copyright © 2013 John Wiley & Sons, Ltd.     

基于微形态理论的各向异性散体波动分析

基于散粒体微观力学理论,忽略颗粒转动引起的相对位移,考虑颗粒接触的组构各向异性,根据宏微观能量守恒推导得到了散体材料各向异性微形态本构关系,进而通过单位接触方向积分的递推公式推导出了各向异性本构张量表达式;在此基础上,根据哈密顿原理得到了各向异性散体材料的运动平衡方程和边界条件,从而求得了平面波在各向异性散粒体中的传播规律和频散关系,最后对波的频散关系和频率带隙进行了详细的参数分析。研究表明：该模型预测了散体中包含3类12种位移波：3种纵波、6种横波和3种平面内横向剪切波;横观各向同性条件下,接触各向异性参数a20越大,纵波和横波的频率越大,而平面内横向剪切波的频率越小;正交各向异性条件下,随着接触各向异性参数a22的增大,与2方向运动相关的横波频率增大,而与3方向运动相关的横波频率则减小;但a22的变化对纵波频率影响很小。材料各向异性程度对横波带宽影响不大,但对纵波带宽影响较大：a20的增大使得声?光学波间的带宽减小,而光学波间的带宽增大,当a20>0.84时,声?光学波间的带隙消失;但是a22的增大则使得声?光学波间的带宽增大,而光学波间的带宽减小。退化为各向同性模型后,预测3类波的频散曲线与其他各向同性模型的结果基本一致。     

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.     

Microstructural deformation mechanisms of unsaturated granular soils

A discrete model for unsaturated granular soils has been developed. Three discrete entities have been defined: particles, water menisci and pores. Local interaction forces and water transfer mechanisms have been integrated into a model through the appropriate equilibrium and balance equations. The results of several numerical tests using this model have been described and discussed. Simulations include wetting and drying under load tests, the application of suction cycles and the effect of a deviatoric stress ratio on wetting‐induced collapse. The model reacts just as true granular soil samples behave in laboratory tests. The model provides a new insight into the internal mechanisms leading to large‐scale features of behaviour such as wetting‐induced collapse or the increase in soil strength provided by suction. The paper also stresses that matric suction changes acting on a granular structure are capable of explaining most of the macroscopic features of stress–strain behaviour. Copyright © 2002 John Wiley & Sons, Ltd.     

Dilatancy of granular materials in a strain space multiple mechanism model

A granular material consists of an assemblage of particles with contacts newly formed or disappeared, changing the micromechanical structures during macroscopic deformation. These structures are idealized through a strain space multiple mechanism model as a twofold structure consisting of a multitude of virtual two‐dimensional mechanisms, each of which consists of a multitude of virtual simple shear mechanisms of one‐dimensional nature. In particular, a second‐order fabric tensor describes direct macroscopic stress–strain relationship, and a fourth‐order fabric tensor describes incremental relationship. In this framework of modeling, the mechanism of interlocking defined as the energy less component of macroscopic strain provides an appropriate bridge between micromechanical and macroscopic dilative component of dilatancy. Another bridge for contractive component of dilatancy is provided through an obvious hypothesis on micromechanical counterparts being associated with virtual simple shear strain. It is also postulated that the dilatancy along the stress path beyond a line slightly above the phase transformation line is only due to the mechanism of interlocking and increment in dilatancy due to this interlocking eventually vanishing for a large shear strain. These classic postulates form the basis for formulating the dilatancy in the strain space multiple mechanism model. The performance of the proposed model is demonstrated through simulation of undrained behavior of sand under monotonic and cyclic loading. Copyright © 2010 John Wiley & Sons, Ltd.     

A numerical representation of fracturing granular materials

This paper describes the computer algorithms used in a numerical simulation of the compression of an aggregate of crushable grains. It has been used in a model for the evolution of a granular medium under one-dimensional compression, in which the probability of fracture for individual particles is a function of applied stress, particle-size and co-ordination number. The information relating to the particles is represented in a compact way on the computer which allows the number of particles produced to become sufficiently large for satisfactory comparisons to be made with experimental data and which allows information, such as the positions and sizes of the particles, to be easily extracted. An algorithm based on the representation is used to locate neighbouring particles in a way which does not deteriorate unacceptably in terms of speed as the number of particles increases. © 1997 by John Wiley & Sons, Ltd.     

Micromechanical analysis of failure propagation in frictional granular materials

The extent to which the evolution of instabilities and failure across multiple length scales can be reproduced with the aid of a bifurcation analysis is examined. We adopt an elastoplastic micropolar constitutive model, recently developed for dense cohesionless granular materials within the framework of thermomicromechanics. The internal variables and their evolution laws are conceived from a direct consideration of the dissipative mechanism of force chain buckling. The resulting constitutive law is cast entirely in terms of the particle scale properties. It thus presents a unique opportunity to test the potential of micromechanical continuum formulations to reproduce key stages in the deformation history: the development of material instabilities and failure following an initially homogeneous deformation. Progression of failure, initiating from frictional sliding and rolling at contacts, followed by the buckling of force chains, through to macroscopic strain softening and shear banding, is reproduced. Bifurcation point, marking the onset of shear banding, occurred shortly after the peak stress ratio. A wide range of material parameters was examined to show the effect of particle scale properties on the progression of failure. Model predictions on the thickness and angle of inclination of the shear band and the structural evolution inside the band, namely the latitudinal distribution of particle rotations and the angular distributions of contacts and the normal contact forces, are consistent with observations from numerical simulations and experiments. Copyright © 2009 John Wiley & Sons, Ltd.     

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。     

粒状材料的强度与变形

颗粒破碎的特征表明,颗粒破碎具有分形特征,是影响粒状材料变形与强度的主要因素,根据颗粒破碎的分形模型可以建立粒状材料的变形与强度理论。假定粒状材料是均匀的D维分形体,由此导出粒状材料的抗张强度公式,并用来估算颗粒在给定压力下的破碎几率。颗粒破碎增加了单位体积颗粒的表面积,即颗粒的比表面能量增加,根据颗粒破碎过程中的能量守恒导出粒状材料一维压缩变形的表达式。     

易破碎粒状材料本构研究

粒状材料被广泛地应用到土木工程的各个领域。大部分粒状材料在外力作用下较容易产生颗粒破碎,颗粒破碎对材料的力学性能有很大的影响。为了更好地描述易破碎粒状材料的力学特性,基于弹塑性力学和临界状态土力学开发了一种能够考虑颗粒破碎效应的本构模型。此本构模型能够考虑在剪应力和压应力作用下引起的颗粒破碎对粒状材料力学性能的影响。为了考虑颗粒破碎的影响,基于对Cambria 砂的高压试验,得出了临界状态线位置与消耗塑性功之间的关系,并称之为“破碎方程”。此本构模型拥有双屈服面,分别考虑剪切和等向压缩产生的塑性变形。通过试验结果与数值计算结果的对比得出,新的本构模型能较好地描述易破碎粒状材料的力学特性     

Local stress analysis in granular materials at a mesoscale

The purpose of this paper is to contribute to the change of scale techniques developed for granular materials. The proposed approach consists in considering an intermediate scale between the macroscales and microscales, called the mesoscale, using the classical homogenization scheme. In this approach, the mesoscale for 2D granular materials was defined at the level of local volumes, called mesodomains, which are local closed structures composed of particles in contact. In this paper, we focused on defining a local stress field at this scale. Two different methods are proposed, both based on the equivalent continuum mean stress but using different approximations of the mean stress tensor for each mesodomain. The two proposed methods were then compared to each other. Analyses performed on the stress field at the mesoscale show that this local field is heterogeneous and, in particular, that its heterogeneity is significantly structured at this scale. The distribution of the local mean stress (first invariant of the local stress tensor) is uniform in any mesodomain, whereas the distribution of the stress deviator (second invariant of the deviatoric part of the local stress tensor) is significantly dependent on the elongation direction and on the elongation degree of the mesodomains. The local stress ratio (ratio of the stress deviator to the mean stress) is higher within the mesodomains that are elongated in the global compression direction than that within the ones elongated in the global extension direction. Copyright © 2011 John Wiley & Sons, Ltd.     

Breakage and deformation mechanisms of crushable granular materials

Biaxial compressional tests with two types of stress paths were carried out on an assembly of round bars, which can be crushed to investigate the breakage and deformation mechanisms of granular materials at the mesoscale. The following was found experimentally: (1) upon loading, the crushable rods slide, rotate and break, and finally the breakage band forms for the two types of stress paths and different stress states; and (2) for the axial loading stress path, the round rods mainly fail in the vertically split mode and laterally crushed mode. However, for the lateral unloading stress path, the round rods fail with the combination mode of locally crushed and vertically split.