A predictive deep learning framework for path-dependent mechanical behavior of granular materials

As we transition into an era of data generation and collection, empirical summaries in the classical continuum modeling of granular materials cannot take full advantage of the increasingly larger data sets. This work presents a data-driven model for modeling granular materials, with the material data being extracted from discrete element method (DEM) simulations. A long short-term memory (LSTM) network is then employed to learn the mechanical behaviors of granular materials from the material dataset. Particular emphasis is placed on three elements: modification of LSTM unit cell, phase space sampling, and material history parameterization. The LSTM unit cell is modified so that the initial hidden state can be specified as the initial states of granular materials. Massive DEM simulations are performed to consider the effects of particle size distribution, initial density, confining pressure, and loading path on the mechanical behaviors of granular materials. The history-dependency of the granular materials is well represented by the architecture of the LSTM network and internal variable-based history parameterization. We compare the model predictions against DEM simulations to assess the performance of the proposed data-driven model. The results demonstrate that the model can predict the material behaviors of granular materials with different microstructures and initial states and reproduce the material responses under complex nonmonotonic loading paths. This data-driven model exhibits good generalization ability and high prediction accuracy in various situations.

     

颗粒材料数值样本的坐标排序生成技术

颗粒材料离散颗粒模型的数值模拟结果与颗粒材料的数值样本密切相关,随着离散单元在颗粒材料数值模拟领域的广泛应用,颗粒材料的数值样本生成技术日益受到重视。基于RSA模型研究如何使随机生成的颗粒材料更密实,对均匀颗粒而言亦即如何在指定区域内生成更多的颗粒,讨论了4类修正方案,并建议了一种基于坐标排序的样本生成技术。研究表明,在传统的颗粒体随机生成技术基础上,通过对随机生成的x坐标序列或y坐标序列进行排序,可使生成的颗粒材料数值样本更密实。     

Unified discrete-element approach applying arbitrary undrained loading paths in element testing for granular soils

The discrete element method (DEM) is crucial in investigating and modeling the elementary behavior of granular materials under varying loading conditions, especially those that cannot be adequately investigated via conventional laboratory testing. However, the application of the DEM in simulations that involve complex loading paths under undrained conditions is scarce, primarily owing to the inability to maintain a constant-volume condition. This paper presents a unified discrete element approach that can apply arbitrary loading paths while satisfying the equivalent undrained condition. The proposed method comprises two parts: (1) a novel strategy that determines the virtual pore pressure under complex undrained loading conditions, and (2) an advanced undrained servomechanism that can simultaneously control each stress component independently. Numerical algorithms corresponding to three new undrained loading paths, that is, true triaxial test, rotational shear, and traffic loading path that have never been simulated using DEM are successfully implemented in a unified manner. Macroscale simulation results under these loading paths are qualitatively in good agreement with their experimental counterparts, thereby confirming the practicality and robustness of the proposed approach. Furthermore, in-depth discussions on the DEM results from these three new loading paths are presented from microscopic perspective.     

Three-dimensional discrete element method parallel computation of Cauchy stress distribution over granular materials

The paper presents Cauchy stress tensor computation over parallel grids of message passing interface (MPI) parallel three-dimensional (3D) discrete element method (DEM) simulations of granular materials, considering spherical and nonspherical particles. The stress tensor computation is studied for quasi-static and dynamic conditions, and its resulting symmetry or asymmetry is discussed within the context of classical continuum mechanics (CCM), granular materials mechanics (GMM), and micropolar continuum mechanics (MCM). The average Cauchy stress tensor computation follows Bagi's and Nicot's formulations and is verified within MPI parallel 3D DEM simulations involving dynamically adaptive compute grids. These grids allow calculation of temporal and spatial distributions of stress across granular materials under static and dynamic conditions. The vertical stress component in gravitationally deposited particle assemblies exhibits nonuniform spatial distributions under static equilibrium, and its zone of maximum value changes during the process of gravitational pluviation and collapse. These phenomena reveal a microstructural effect on stress distribution within granular materials that is attributed to their discrete particulate nature (particle size, shape, gradation, boundary conditions, etc).     

Side resistance of drilled shafts in granular soils investigated by DEM

The paper presents a numerical study on the side resistance of a drilled shaft in granular materials. The numerical result is used to develop new design equations for the side resistance of drilled shafts in granular soils. The Discrete Element Method (DEM) is used to model a drilled shaft in granular material. The granular material is represented as assemblies of ellipsoidal particles. Nominal side resistance is represented as the product of a parameter (β) and vertical stress. The numerical result shows that the relationship between β and void ratio can be described by a hyperbolic function for a given vertical stress. DEM result is also compared with three design equations. Although these design equations capture the decrease of β with depth, deviation is observed between the DEM results and the design equations. Finally, new design equations based on state parameter are proposed.     

A 4th order fabric tensor approach applied to granular media

In this paper, we propose a micromechanical approach of the behavior of granular media, which takes into account the anisotropy by means of a fourth order fabric tensor. The proposed approach is implemented in an homogenization scheme based on Voigt and Reuss localization assumption. The fabric tensor-based approach is then combined with a new kinematic localization rule and yields a general homogenization scheme for anisotropic granular media.     

离散单元法对粒状土的微观特性研究探讨

粒状土的微观结构和微观力学被认为是其宏观力学和体积特性的内在根本因素,近年来得到越来越多的关注和研究。离散单元法作为一种研究颗粒材料的数值模拟计算方法,比试验方法快捷、简便、经济,而且能够容易得到在实验室试验中很难或无法得到的更多重要的微观结构和微观力学的信息,近年来得到越来越多应用。本文介绍了离散单元法对土的微观特性研究的一些最新方法和进展,对数值建模中的一些重要方面如比重(质量)放大、树脂薄膜模拟等方面进行了阐述,对离散单元法在土的微观结构分析(如颗粒旋转、颗粒位移、中尺度孔隙率分布)的一些最新研究作了分析和介绍。分析表明,离散单元法是研究粒状土的微观特性的一个有力工具,可以对土的宏观特性从微观角度得到更好的解释和认识。     

Static and kinematic damage characterization in structured sand

Damage is the key process controlling the behavior of cemented geomaterials, such as structured sand. Damage characterization of structured sand is studied based on granular material mechanics with the aid of discrete element method (DEM) simulation in this paper. Structured sand is viewed as a mixture of remolded and structured parts, whose behavior is defined by the collective responses of unbonded and bonded contacts, respectively. Based on the cross-scale links between macroscopic quantities (stress and strain) and microscopic quantities (contact force, contact position and relative motion of particles), stresses and strains of the two parts are assembled to arrive at the overall stress and strain of structured sand. The weights of the two parts in stress and strain assembling/partitioning emerge naturally as a stress-based static damage variable and a strain-based kinematic damage variable, respectively, which are then evaluated using the DEM simulation results. The static damage variable captures the role of remolded part in load-bearing structure of structured sand, while the kinematic damage variable describes the spatial geometric configuration of the two parts. Both damage variables increase with deviator strain in a sigmoidal pattern. Directional damage indexes indicate that damage is isotropic from the view of kinematic response, but it is anisotropic if examined from static point of view. The degree of anisotropy in static damage is influenced by external stress conditions and internal microstructure anisotropy. This study provides a physically robust and theoretically rigid framework for the development of a micromechanics-based constitutive model of structured sand.

     

Discrete-Element Computation of Averaged Tensorial Fields in Sand Piles Consisting of Polygonal Particles

This work is a contribution to the understanding of the mechanical properties of non-cohesive granular materials in the presence of friction and a continuation of our previous work (Roul et al. 2010) on numerical investigation of the macroscopic mechanical properties of sand piles. Besides previous numerical results obtained for sand piles that were poured from a localized source (“point source”), we here consider sand piles that were built by adopting a “line source” or “raining procedure”. Simulations were carried out in two-dimensional systems with soft convex polygonal particles, using the discrete element method (DEM). First, we focus on computing the macroscopic continuum quantities of the resulting symmetric sand piles. We then show how the construction history of the sand piles affects their mechanical properties including strain, fabric, volume fraction, and stress distributions; we also show how the latter are affected by the shape of the particles. Finally, stress tensors are studied for asymmetric sand piles, where the particles are dropped from either a point source or a line source. We find that the behaviour of stress distribution at the bottom of an asymmetric sand pile is qualitatively the same as that obtained from an analytical solution by Didwania and co-workers (Proc R Soc Lond A 456:2569–2588, 2000).     

Study on the particle breakage of ballast based on a GPU accelerated discrete element method

Breakage of particles will have greatly influence on mechanical behavior of granular material(GM)under external loads,such as ballast,rockfill and sand.The discrete element method(DEM)is one of the most popular methods for simulating GM as each particle is represented on its own.To study breakage mechanism of particle breakage,a cohesive contact mode is developed based on the GPU accelerated DEM code-Blaze-DEM.A database of the 3D geometry model of rock blocks is established based on the 3D scanning method.And an agglomerate describing the rock block with a series of non-overlapping spherical particles is used to build the DEM numerical model of a railway ballast sample,which is used to the DEM oedometric test to study the particles’breakage characteristics of the sample under external load.Furthermore,to obtain the meso-mechanical parameters used in DEM,a black-analysis method is used based on the laboratory tests of the rock sample.Based on the DEM numerical tests,the particle breakage process and mechanisms of the railway ballast are studied.All results show that the developed code can better used for large scale simulation of the particle breakage analysis of granular material.     

Three dimensional steady-state locus for dry monodisperse granular materials: DEM numerical results and theoretical modelling

In this paper, steady-state conditions for ideal monodisperse dry granular materials are both theoretically and numerically analysed. A series of discrete element (DEM) numerical simulations have been performed on a periodic cell by imposing stress paths characterized by different Lode angles, pressures, and deviatoric strain rates. The dependence of the material response on both inertial number and loading path has been discussed in terms of void ratio, fabric, and granular temperature. DEM numerical results have been finally compared with the prediction of an already conceived model based on both kinetic and critical state theories, here suitably modified to account for three-dimensional conditions.     

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。     

3D analysis of kinematic behavior of granular materials in triaxial testing using DEM with flexible membrane boundary

This paper describes the constitutive behavior and particle-scale kinematics of granular materials in three-dimensional (3D) axisymmetric triaxial testing using discrete element method (DEM). PFC3D code was used to run the DEM simulations using a flexible membrane boundary model consisting of spherical particles linked through flexible contact bonds. The overall deformation behavior of the specimen was then compared with the specimen with rigid boundary and experimental measurements. Computed tomography was used to track the evolution of particle translation and rotation within a laboratory triaxial specimen in 3D. The DEM model of the flexible membrane specimen successfully predicted the stress–strain behavior when compared with laboratory experiment results at different confining pressures. The DEM results showed that the rigid specimen applies a uniform deformation and leads to non-uniformities in the confining stress along the particle-boundary interface in the lateral direction. In contrast, the flexible specimen better replicates the uniformly applied confining stress of a laboratory triaxial experiment. The 3D DEM simulations of the specimen with flexible membrane overpredicted particle translation and rotation in all directions when compared to a laboratory triaxial specimen. The difference between the particle translation and rotation distributions of DEM specimens with rigid and flexible membrane is almost negligible. The DEM specimen with flexible membrane produces a better prediction of the macroscopic stress–strain behavior and deformation characteristics of granular materials in 3D DEM simulations when compared to a specimen with rigid membrane. Comparing macroscale response and particle-scale kinematics between triaxial simulation results of rigid versus flexible membrane demonstrated the significant influence of boundary effects on the constitutive behavior of granular materials.     

Analysis of soil‐structural interface behavior using three‐dimensional DEM simulations

The shear behavior at the interface between the soil and a structure is investigated at the macroscale and particle‐scale levels using a 3‐dimensional discrete element method (DEM). The macroscopic mechanical properties and microscopic quantities affected by the normalized interface roughness and the loading parameters are analyzed. The macro‐response shows that the shear strength of the interface increases as the normalized roughness of the interface increases, and stress softening and dilatancy of the soil material are observed in the tests that feature rough interfaces. The particle‐scale analysis illustrates that a localized band characterized by intense shear deformation emerges from the contact plane and gradually expands as shearing progresses before stabilizing at the residual stress state. The thickness of the localized band is affected by the normalized roughness of the interface and the normal stress, which ranges between 4 and 5 times that of the median grain diameter. A thicker localized band is formed when the soil has a rough shearing interface. After the localized band appears, the granular material structuralizes into 2 regions: the interface zone and the upper zone. The mechanical behavior in the interface zone is representative of the interface according to the local average stress analysis. Certain microscopic quantities in the interface zone are analyzed, including the coordination number and the material fabric. Shear at the interface creates an anisotropic material fabric and leads to the rotation of the major principal stress.     

Deformation characteristics of inherently anisotropic granular media under repeated traffic loading: a DEM study

Acta Geotechnica - The cardioid-shaped loading path induced by moving traffic has been reproduced in the virtual element test of granular media using the discrete element method (DEM). The DEM...     

DEM investigations of internal erosion: Grain transport in the light of micromechanics

Internal erosion by suffusion can change dramatically the constitutive behavior of granular materials by modifying the fabric of granular materials. In this study, the effect of an internal fluid flow on granular materials is investigated at the material point scale using the numerical coupling between a discrete element method (DEM) and a pore-scale finite volume (PFV) coupling scheme. The influence of the stress state and the hydraulic loading (direction and intensity) on the occurrence of grain transport in dense widely graded granular samples is thus investigated and interpreted in terms of micromechanics. In particular, it is shown that grain transport is increased when the macroscopic flow direction is aligned with the privileged force chain orientation. The stress-induced microstructure modifications are shown to influence the transport distances by controlling the number of rattlers.     

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.     

Discrete element modeling for predicting breakage behavior and fracture energy of a single particle in a jaw crusher

In the present study, Discrete Element Method (DEM) technique was applied to model the fracture behavior of a single spherical and cubic rock in a laboratory jaw crusher. The rocks studied were modeled as granular assemblies located between two jaws, and their fracture mechanism was studied. To verify the obtained results, the spherical and cubic specimens produced from Dokoohak Limestone and Dehbeed Granite were studied and the energy applied by the jaws was compared to those of the fracture energy estimated by the single particle breakage analysis. There is fairly good agreement between the energy acquired from the DEM model and the single particle fracture energy of the spherical rocks. It appears that DEM is a suitable method for predicting the crushing energy of the spherical rocks in the jaw crusher. The fracture behavior of the crushed rocks was examined and compared by the results obtained from the DEM model. The tensile mode of fracture occurring in the spherical rocks is well presented by the discrete element modeling. However, the DEM technique is not capable of modeling the delamination mode occurring in the cubic rocks.