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.     

非饱和土三轴压缩应力路径试验的数值模拟研究

应力路径对土的强度和变形性质具有重要影响。相对于饱和土而言,控制吸力条件下的非饱和土三轴压缩状态的应力路径研究更加复杂。随着非饱和土本构理论的不断发展,理论和试验研究结果表明,非饱和土弹塑性本构模型可以用来近似地描述非饱和土的强度和变形性质。因而,运用非饱和土弹塑性本构模型对控制吸力条件下的3种非饱和土三轴压缩应力路径试验进行数值模拟是一种有效的理论研究手段。采用Barcelona模型能够对此类试验进行较好的数值模拟,其研究结果表明,在控制吸力条件的三轴压缩状态下应力路径对非饱和土的强度和变形性质具有重要影响。     

DEM investigation of the effect of intermediate principle stress on particle breakage of granular materials

This study investigates the influence of the intermediate principle stress on the particle breakage of granular materials. The crushable agglomerate method is applied to model soil particles and numerical true triaxial tests were carried out. The results show that particle breakage increases with increasing b value, the relationship of which follows an exponential function and agrees well with previous experimental results. More importantly, the study found that the relationship between particle breakage and total energy input is independent of the intermediate principle stress, which provides a good basis for the constitutive modeling of granular materials.     

DEM analyses of one-dimensional compression and collapse behaviour of unsaturated structural loess

Natural loess is a kind of under-consolidated and unsaturated loose granulates (silts) with its microstructure characterized with large voids and inter-particle cementation. This paper presents a distinct element method (DEM) to investigate its macro- and micro-mechanical behaviour (compression and collapse behaviour) under one-dimensional (1D) compression condition. A relationship between bond strength in DEM model and initial water content is used to develop a bond contact model for loess. Then, DEM structural loess samples are prepared by the multi-layer under-compaction method, and cemented with the bond contact model. The effect of water content and void ratio on compression and collapse behaviour of loess is numerically investigated by simulating 1D compression and wetting tests on the DEM material. The DEM results agree qualitatively with available experimental observations in literatures. The wetting-induced deformation is independent of the sequence of wetting and loading under 1D compression condition. The macroscopic yielding and collapse behaviours are associated with bond breakage on microscopic scale. Moreover, bonds break in one of the two failure types in the simulations, i.e. tensile failure and shear failure (compression-shear failure and tension-shear failure), with bonds broken firstly mainly due to tension followed by shear when the samples are compressed, while mainly due to shear when the samples are wetted under a certain pressure. In addition, the contact orientations and deviator fabrics of contacts under 1D compression and wetting were also investigated.     

Fibre-reinforcement of granular materials: DEM visualisation and analysis

Mechanical properties of granular materials can be significantly improved by the inclusion of small amounts of short synthetic fibres. This phenomenon has been experimentally studied before by many researchers who have found that the shear strength of a granular material can be significantly improved. This study presents a visualisation of the phenomenon using discrete element method (DEM) simulations of direct shear tests conducted on mixtures of an idealised granular material and randomly oriented fibres. Snapshots showing the deformation of the samples, the velocity vectors of the particles and the force chains produced inside the samples are presented at different stages of the tests. Changes in shear strength and porosity are also illustrated. It was found that the reinforcement produced depends mostly on the rigidity of the fibres.     

Macroscopic and microscopic behaviors of granular materials under proportional strain path: a DEM study

Under the proportional strain loading path, particle assemblies may exhibit various failure modes. Besides the strain localization, the diffuse failure may also occur under certain conditions. The diffuse failure mode corresponds to a homogeneous occurrence of failure with stress states strictly included within the plastic limit condition. This paper emphasizes the influences of the density degree and the rolling resistance under the strain path. A contact model considering rolling friction is adopted in a discrete element method analysis as an approximate means to account for the effects of particle shape. Mechanical responses indicate that loose assemblies without the rolling resistance are more vulnerable to static liquefaction. A sample with a smaller initial void ratio or larger rolling friction coefficient will reinforce the stability of the structure and reduce the likelihood of failure. For microscopic properties, the evolution of coordination numbers, contact forces, force chains and the anisotropies of the assemblies are explored and discussed. Rotational resistance helps increase the shear stress of the granular material, and the microscopic parameters indicate that the assembly has a strong anisotropy and a stable structure to resist the increasing loading.     

DEM studies on the effect of particle breakage on the critical state behaviours of granular soils under undrained shear conditions

Acta Geotechnica - A number of discrete element analyses of undrained triaxial shear tests on crushable assemblies are performed using 3-dimensional particle flow code (PFC3D). The undrained shear...     

Correlation of fabric tensors for granular materials using 2D DEM

Acta Geotechnica - Soil fabric anisotropy can be quantitatively assessed by means of fabric tensors introduced as internal variables in constitutive models and defined by unit vectors along the...     

Three-dimensional DEM investigation of critical state and dilatancy behaviors of granular materials

The critical state is significant to the mechanical behaviors of granular materials and the foundation of the constitutive relations. Using the discrete element method (DEM), the mechanical behaviors of granular materials can be investigated on both the macroscopic and microscopic levels. A series of DEM simulations under true triaxial conditions have been performed to explore the critical state and dilatancy behavior of granular materials, which show the qualitatively similar macroscopic responses as the experimental results. The critical void ratio and stress ratio under different stress paths are presented. A unique critical state line (CSL) is shown to indicate that the intermediate principal stress ratio does not influence the CSL. Within the framework of the unique critical state, the stress–dilatancy relation of DEM simulations is found to fulfill the state-dependent dilatancy equations. As a microscopic parameter to evaluate the static determinacy of the granular system, the redundancy ratio is defined and investigated. The results show that the critical state is very close to the statically determinate state. Other particle-level indexes, including the distribution of the contact forces and the anisotropies, are carefully investigated to analyze the microstructural evolution and the underlying mechanism. The microscopic analysis shows that both the contact orientations and contact forces influence the mechanical behaviors of granular materials.     

Resilient and permanent deformation of unsaturated unbound granular materials under cyclic loading by the large-scale triaxial tests

Acta Geotechnica - The road base and subbase are normally situated above the underground water table and thus in the unsaturated state. To study the cyclic behavior of unbound granular materials...     

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.     

Fabric evolution of granular materials along imposed stress paths

The stress–strain behavior of a granular material is dominated by its internal structure, which is related to the spatial connectivity of particles, and the force chain network. In this study, a series of discrete element simulations were carried out to investigate the evolution of internal structure and force chain networks in initially isotropic granular materials along various imposed stress paths. The fabric tensor of the strong sub-network, which is the bearing network toward loading, can be related to the applied stresses uniquely. The principal directions of fabric tensor of the strong sub-network coincide with those of stress tensor during the loading process in the Lode coordinate system. The fabric of the whole contact network in the pre- and post-peak deformation stages can be related to the applied stresses as \(q_{\phi } = B\left( {q/p} \right)^{z}\) (B and z are constants depending on loading condition, such as the stress paths and mean stress level) and \(\phi_{1} :\phi_{2} :\phi_{3} \approx \left( {\sigma_{1} } \right)^{0.4} :\left( {\sigma_{2} } \right)^{0.4} :\left( {\sigma_{3} } \right)^{0.4}\), respectively. At the critical stress state, the deviator of fabric tensor of the strong sub-network is much larger than that of the whole contact network. When plotted on the π-plane, the fabric state of the strong sub-network can be expressed as a Lade’s surface, while the fabric state of the whole network corresponds to an inverted Lade’s surface.     

DEM filtration modelling for granular materials: Comparative analysis of dry and wet approaches

A detailed study comparing two – dry and wet – numerical approaches to model filtration processes at stake in actual granular filters is presented using the discrete element method (DEM). In the first approach, the migration of fines is provided by gravitational forces, while in the second, hydrodynamic forces induce their movement. Numerical filtration tests were performed on granular filters involving materials with different gradings and porosities. The study demonstrated that the wet filtration approach generates higher tortuosity due to the possibility for fines to deviate from direct paths towards more open sideways. It leads to a lower coefficient of retention for the filter than if it were characterised using a dry filtration approach. However, the intensity of this feature greatly depends on the grading and the porosity of the granular filter. Finally, an enhanced dry filtration model designated as the “equivalent cyclic wet filtration model” is presented, which better mimics the results obtained through the preferable wet filtration model compared to the original dry filtration model. This new model constitutes a valuable alternative tool for studies of filtration properties in granular materials.