Response Of Granular Materials Research Articles

Effects of interparticle friction on the response of 3D cyclically compressed granular material

We numerically study the effect of inter-particle friction coefficient on the response to cyclical pure shear of spherical particles in three dimensions. We focus on the rotations and translations of grains and look at the spatial distribution of these displacements as well as their probability distribution functions. We find that with increasing friction, the shear band becomes thinner and more pronounced. At low friction, the amplitude of particle rotations is homogeneously distributed in the system and is therefore mostly independent from both the affine and non-affine particle translations. In contrast, at high friction, the rotations are strongly localized in the shear zone. This work shows the importance of studying the effects of inter-particle friction on the response of granular materials to cyclic forcing, both for a better understanding of how rotations correlate to translations in sheared granular systems, and due to the relevance of cyclic forcing for most real-world applications in planetary science and industry.

Deep Learning Predicts Stress–Strain Relations of Granular Materials Based on Triaxial Testing Data

This study presents an AI-based constitutive modelling framework wherein the prediction model directly learns from triaxial testing data by combining discrete element modelling (DEM) and deep learning. A constitutive learning strategy is proposed based on the generally accepted frame-indifference assumption in constructing material constitutive models. The low-dimensional principal stress-strain sequence pairs, measured from discrete element modelling of triaxial testing, are used to train recurrent neural networks, and then the predicted principal stress sequence is augmented to other high-dimensional or general stress tensor via coordinate transformation. Through detailed hyperparameter investigations, it is found that long short-term memory (LSTM) and gated recurrent unit (GRU) networks have similar prediction performance in constitutive modelling problems, and both satisfactorily predict the stress responses of granular materials subjected to a given unseen strain path. Furthermore, the unique merits and ongoing challenges of data-driven constitutive models for granular materials are discussed.

Erosional response of granular material in landscape models

Abstract. Tectonics and erosion–sedimentation are the main processes responsible for shaping the Earth's surface. The link between these processes has a strong influence on the evolution of landscapes. One of the tools we have for investigating coupled process models is analog modeling. Here we contribute to the utility of this tool by presenting laboratory-scaled analog models of erosion. We explore the erosional response of different materials to imposed boundary conditions, trying to find the composite material that best mimics the behavior of the natural prototype. The models recreate conditions in which tectonic uplift is no longer active, but there is an imposed fixed slope. On this slope the erosion is triggered by precipitation and gravity, with the formation of channels in valleys and diffusion on hillslope that are functions of the analog material. Using digital elevation models (DEMs) and a laser scan correlation technique, we show model evolution and measure sediment discharge rates. We propose three main components of our analog material (silica powder, glass microbeads and PVC powder; PVC: polyvinyl chloride), and we investigate how different proportions of these components affect the model evolution and the development of landscapes. We find that silica powder is mainly responsible for creating a realistic landscape in the laboratory. Furthermore, we find that varying the concentration of silica powder between 40 wt % and 50 wt % (with glass microbeads and PVC powder in the range 35 wt %–40 wt % and 15 wt %–20 wt %, respectively) results in metrics and morphologies that are comparable with those from natural prototypes.

Evolution of shear wave velocity during triaxial compression

Accurate design of geotechnical structures requires precise estimation of the shear wave velocity (Vs) and the small-strain shear modulus. However, the interpretation of Vs data measured in deformed/sheared soil has not been extensively considered. This study used a triaxial apparatus equipped with planar piezoelectric transducers to monitor the evolution of Vs during triaxial compression of cohesionless soils. Recognizing that the grain shape and surface characteristics affect the overall mechanical response of granular materials, various natural sands and glass bead samples were considered. Discrete element method (DEM) simulations using spherical particles were carried out to compute particle-scale responses that cannot be measured in the laboratory. The experimental results revealed that the Vs values for samples with different initial densities tend to approach one another and have similar values (merge) at large axial strains. This merging occurs at a lower strain level for spherical particles in comparison with non-spherical particles. The linear Vs-void ratio relationship, which is often developed and used for homogeneous and isotropic stress states, is no longer applicable during shearing. It is the mean coordination number that dictates the evolution of Vs during triaxial compression. Furthermore, the axial strain at which the peak Vs is achieved is found to be comparable to the axial strain at which specimen dilation takes place.

Evaluating the particle rolling effect on the characteristic features of granular material under the critical state soil mechanics framework

The discrete element method (DEM) has been extensively used to capture the macroscopic and particulate response of granular materials. Although particle rolling (i.e. controlled by rolling resistance) has been acknowledged as a major contributing factor towards micro-mechanical behaviour of idealized spherical granular material, its influence on characteristic behaviour has not been thoroughly investigated within critical state soil mechanics (CSSM) framework. For instance, the influence of particle rolling on characteristic features of undrained and drained behaviour (e.g. phase transformation, characteristic state, instability, dilatancy, critical state) and the state parameter, (ψ) has not been captured. In this study, a series of constant volume (CV) and drained triaxial compression simulations were undertaken using a rolling resistance linear contact model, deployed within a DEM software. The CSSM framework was centrally used to assess the influence of particle rolling tendencies/resistance on CV and drained behaviours from both a macro- and micro-mechanical standpoint. The study advanced the current understanding of the influence of rolling resistance on CS-related behaviour.

Resilient behavior of coarse granular materials in three dimensional anisotropic stress state

The coarse granular materials in the pavement base and subbase layers are generally in the stress state of three dimensional anisotropy, while most previous experimental researches regarding the base and subbase materials focused on the isotropic or axisymmetric K0 stress conditions. In this study, the resilient characteristics of unbound granular materials in initial three dimensional anisotropic stress states were investigated through an electro-mechanical true triaxial apparatus. The influences of initial shear stress, qini, coefficient of intermediate principal stress, b, amplitude of cyclic major principal stress, σ1ampl, and moisture content on the resilient responses of granular materials were investigated. Test results reveal that the resilient response of unbound granular materials is strongly affected by the three dimensional stress anisotropy in the saturated condition. With the increase of b from 0 to 0.8, a significant reduction of Mr occurs, and this reduction becomes intensified as qini increases. It is also found that Mr is increased by the increase of qini for almost all tests, and the increasing rate varies at different σ1ampl, b and moisture content values. Based on the experimental results, an empirical model to predict resilient modulus is proposed incorporating the effects of initial three dimensional stress anisotropy, which is expected to serve as a basic model to calculate the resilient modulus of granular materials in three dimensional stress state.

Macro and meso dynamic response of granular materials in ballastless track subgrade for high-speed railway

Abstract Considering the discrete and stochastic properties of granular materials, a two-dimensional numerical model was established to study the dynamic behavior of high-speed railway (HSR) ballastless track subgrade by using finite difference-discrete element (FDM-DEM) coupling method. Combined with on-site vibration test results in macroscopic scale, the mesoscopic vibration response of subgrade granular materials was analyzed under different speed levels. Some unusual phenomena were observed as follow: 1). In the surface layer (i.e., the top area of the subgrade, thickness = 0.4 m), particles showed a very wide response band in the frequency domain (up to 130 Hz), even beyond the maximum frequency of train loading (60 Hz). It was found that some particles in the surface layer produced not only forced vibration, but also local random vibration. However, the bottom layer particles (i.e., the area under the surface layer, thickness = 2.3 m) were only active within 40 Hz. 2) Force chains in the granular aggregate were disappeared and rebuilt synchronously in the dynamic loading process. A typical mode of force chain weakening was described in meso scale. 3) Particles at interface region between the surface and bottom layer exhibited severe local vibration amplification when the train speed level was higher than 300 km/h.

Anisotropy of elastic wave velocity influenced by particle shape and fabric anisotropy under K0 condition

Non-cohesive granular materials exhibit fabric-induced anisotropy of small-strain stiffness. The stiffness anisotropy is often measured using dynamic wave measurements in the laboratory. It is widely accepted that elastic wave velocities are influenced by stress state, while the role of particle shape in the wave velocity anisotropy, and thus the stiffness anisotropy, has not been fully understood. The difficulty arises partially from the incomplete understanding of particle-scale responses of granular materials. Considering 1D vertical compressoin with zero lateral strains (K0 condition) analogue to in-situ ground, this contribution performs wave propagation simulations using discrete element method and explores how particle shape and packing characteristics influence the anisotropy of elastic wave velocity. Sphere clumps with various aspect ratios are used. The orientation of the particle major axis is varied systematically by inhibiting particle rotation during dry-pluviation process. The simulation results reveal that the wave velocity anisotropy is largely affected by the combined effect of the particle aspect ratio and the orientation of particle major axis. Micromechanical analyses on assemblies of sphere clumps and ellipsoids shed light on the importance of the inter-particle contact stiffness, in addition to the particle aspect ratio and fabric, to determine the wave velocity anisotropy when non-spherical particles are used.

Partially drained cyclic behaviour of granular fill material in triaxial condition

The dynamic responses of granular materials subjected to cyclic loading under partially drained condition were seldom investigated, though the partially drained condition is commonly existing for the granular materials that locate nearby the drainage boundaries. Besides, the prevalent studies mainly focus on the liquefaction behaviour of granular materials under high stress levels. In this study, a granular fill material was chosen as testing material. A series of partially drained cyclic triaxial tests was conducted with low level of cyclic loading and high cycle number that are commonly experienced in the geostructures of transportation projects. Note that the cyclic triaxial test under partially drained condition is a model test rather than an element test since the distribution of excess pore water pressure is not homogeneous inside the specimen. The test results show that cyclic loading induces the reconstruction effect on the microstructure of the specimen, thereby changing the trend between permeability and void ratio. Under partially drained condition, the granular fill material normally experiences a sudden decrease of stiffness and a quick increase in deformation during the first cycles of loading, followed by gradually decreasing excess pore water pressure and stabilizing deformation. Importantly, the deformation response of the material can be contributed by two items: (a) that caused by densification effect of applied cyclic loading and (b) that due to the dissipation of excess pore water pressure. Two linear relationships were established to correlate the deformations with excess pore water pressure and applied cyclic loading.

Comparison of undrained behaviors of granular media using fluid-coupled discrete element method and constant volume method

The fluid-coupled discrete element method (DEM) and the constant volume method as two types of discrete modeling methods for fundamental study of undrained responses of granular materials, have been discussed by many researchers. The fluid-coupled DEM, which couples the motions of discrete particles with pore fluid movements, is theoretically robust although it requires a large amount of computation time. As a substitution for the complex fluid-coupled DEM, the constant volume method simulates an undrained condition for a saturated granular material by simply preserving the total volume of a granular assembly without considering interactions between fluids and particles; hence, the validity of its results is questionable. In this paper, the undrained behaviors of granular assemblies simulated using the aforementioned two methods are compared. Based on a comparison of both macroscopic and microscopic responses given by the two methods, it is demonstrated that the constant volume method may reasonably simulate the responses of a loose saturated granular material with very coarse grains, which has a high permeability, and thus a rapid pore pressure equalization. However, it is ineffective in simulating the responses of a loose material with fine components due to its failure to capture the process of a slow dissipation of the excess pore pressure among the individual pores. With regard to the dense material adopted, similar behaviors at the early and intermediate shearing stages given by the two methods are displayed.

Investigations of the effects of particle morphology on granular material behaviors using a multi-sphere approach

This article studies the influences of particle morphology on the behaviors of granular materials at both macroscopic and microscopic levels based on the discrete element method (DEM). A set of numerical tests under drained triaxial compression was performed by controlling two morphological descriptors, i.e. ratio of the smallest to the largest pebble diameter, ξ , and the maximum pebble–pebble intersection angle, β . These descriptors are vital in generating particle geometry and surface textures. It was found that the stress responses of all assemblies exhibited similar behavior and showed post-peak strain-softening. The normalized stress ratio and volumetric strains flatten off and tended to reach a steady value after an axial strain of 40%. While the friction angles at peak state varied with different morphological descriptors, the friction angles at critical state showed no significant variation. Moreover, evolution of the average coordination numbers showed a dramatic exponential decay until an axial strain of about 15% after which it stabilized and was unaffected by further increase of axial strain. In addition, stress ratio q / p and strong fabric parameter ϕ d s / ϕ m s were found to follow an approximately linear relationship for each assembly. These findings emphasized the significance of the influences of particle morphology on the macroscopic and microscopic responses of granular materials.

Effects of material properties on the mobility of granular flow

In this study, we investigate the influence of material properties on the mobility of granular flow through granular column collapse experiments using the Smooth Particle Hydrodynamics method and a continuum constitutive model capable of describing the nonlinear responses of granular materials. Numerical simulations are systematically compared with available experimental data and well-established empirical laws to validate the capability of this numerical approach for simulating the dynamics of granular flow. Based on this validation, a series of numerical experiments is conducted to investigate the effects of strength properties (i.e. friction and dilation), density and stiffness properties (i.e. Young’s modulus and Poisson’s ratio) on the run-out distance and energy evolution of granular flows, which were unclear or contradictorily reported in previous experimental studies. We found that as the friction angle increases, the material is less mobilised and hence the run-out distance is shorter. In addition, a denser state (i.e. more dilation) facilitates its mobilisation associated with a greater volume expansion during the collapse. The density and stiffness properties of granular materials, nonetheless, have negligible effects on the deposit morphology and run-out distance of granular flow. To further quantify the effects of material properties, the run-out scaling law of granular flow, which describes the relationship between the run-out distance and the initial geometry of granular columns, is analysed and shown to be significantly influenced by the friction and dilation of the materials.

Some Remarks on the Equilibrium of Granular Materials Described by Constitutive Relations That Depend on the Gradients of the Density or Volume Fraction

Abstract One of the ways of determining the properties of granular materials is to subject the material to a tri-axial state of stress with three distinct eigenvalues, in a cubical tri-axial testing equipment, the material tested being in a static state. A constitutive relation for granular materials that does not allow the body to be in tri-axial static equilibrium would not be a reasonable model as experiments clearly show that granular materials can exist in such tri-axial states. In this short note, we observe that a large class of models that have been developed and used to describe the response of granular materials will not allow them to be in a static tri-axial state of stress with three different principal stresses.

Numerical investigation of force transmission in granular media using discrete element method

In this paper, a numerical Discrete Element Method (DEM) model was calibrated to investigate the transmission of force in granular media. To this aim, DEM simulation was performed for reproducing the behavior of a given granular material under uniform compression. The DEM model was validated by comparing the obtained shear stress/normal stress ratio with results published in the available literature. The network of contact forces was then computed, showing the arrangement of the material microstructure under applied loading. The number and distribution of the contacts force were also examined statistically, showing that the macroscopic behavior of the granular medium highly depended on the force chain network. The DEM model could be useful in exploring the mechanical response of granular materials under different loadings and boundary conditions.

Investigation of Initial Static Shear Stress Effects on Liquefaction Resistance Using Discrete Element Method Simulations

Prior laboratory and in situ investigations show that monotonic preshearing can have a significant effect on the cyclic response of granular materials. The underlying mechanics that are responsible for these changes in behavior in response to preshearing are not well characterized, however. Herein, we use the discrete-element method (DEM) to simulate undrained monotonic and cyclic simple shear tests with the constant volume method. Through published comparisons to laboratory data, DEM simulations have been shown to reasonably predict the cyclic response of granular materials, making them an appropriate tool for studying the effects of initial static shear stress on liquefaction initiation. Mechanical coordination number and the normal force-weighted fabric tensor are used to describe the evolution of fabric after monotonic preshearing and during cyclic loading. We find that higher initial static shear stress induces smaller cyclic strength in stress-controlled cyclic simple shear tests, but that there is no such effect in strain-controlled cyclic simple shear tests in which the normal force-weighted anisotropy is removed in the first three loading cycles. In addition, the stability of specimens is found to be closely related to pore-pressure increases. Finally, we show that the effect of initial static shear stress on liquefaction resistance is a combination of reduced stability before cyclic loading and accumulated shear strain during cyclic loading.

Strong contacts, connectivity and fabric anisotropy in granular materials: A 3D perspective

The micro-structural fabric and topology play a key role in macroscopic responses of granular materials. Generally, the contact network is formed by connecting centers of interactive particles, which could be divided into strong and weak contact subsets. Different topological, geometrical and mechanical characteristics could be found for the two parts of network, and the threshold is somehow artificial. Based on true triaxial DEM simulation results, this paper focuses on the fabric anisotropies and the connectivity characteristics of strong contact networks distinguished by different contact force thresholds, moreover the roles of particles with different coordination numbers in the strong networks are identified. The strong contact network characterizes the main features of the macro stress tensor and the proper threshold for discriminating strong and weak contact networks falls in a range. Particles connected by 2 contacts are important in forming the strong contact network and reflecting the main features of force anisotropy.

A homogenization equation for the small strain stiffness of gap-graded granular materials

Sandstone usually disintegrates into gap-graded granular materials with a matrix-sustained structure due to weathering factors. This paper presents an investigation on the small strain stiffness of this type of granular materials based on Discrete Element Method (DEM) simulations. Our numerical results indicate the percentage of sliding contact is negligibly small within the small strain range, and the small strain stiffness of fines is well consistent with the widely recognized Hardin’s equation. Both findings confirm the validity of DEM simulations on the study of small strain response of granular materials. The simulation results are further analyzed based on mixture theory. A structure variable is introduced to correlate with the evolution of inter-aggregates structure. This variable is found to increase with the volume fraction of coarse aggregates but is rather independent of the confining stress and the initial void ratio of the fine matrix. Based on the insights drawn from DEM simulations, a homogenization equation is proposed for the small strain stiffness of gap-graded granular soils to reproduce the small strain stiffness of gap-gaped materials observed in our numerical simulations and is further validated by laboratory test data from the literature. The equation can be conveniently incorporated into classical elastoplastic models to model gap-graded granular materials.

Universality of internal structure characteristics in granular media under shear.

We examine the signatures of internal structure emerged from quasistatic shear responses of granular materials based on three-dimensional discrete element simulations. Granular assemblies consisting of spheres or nonspherical particles of different polydispersity are sheared from different initial densities and under different loading conditions (drained or undrained) steadily to reach the critical state (a state featured by constant stress and constant volume). The radial distribution function used to measure the packing structure is found to remain almost unchanged during the shearing process, regardless of the initial states or loading conditions of an assembly. Its specific form, however, varies with polydispersities in both grain size and grain shape. Set Voronoi tessellation is employed to examine the characteristics of local volume and anisotropy, and deformation. The local inverse solid fraction and anisotropy index are found following inverse Weibull and log-normal distributions, respectively, which are unique at the critical states. With further normalization, an invariant distribution for local volume and anisotropy is observed whose function can be determined by the polydispersities in both particle size and grain shape but bears no relevance to initial densities or loading conditions (or paths). An invariant Gaussian distribution is found for the local deformation for spherical packings, but no invariant distribution can be found for nonspherical packings where the distribution of normalized local volumetric strain is dependent on initial states.

Rattler wedging and force chain buckling: metastable attractor dynamics of local grain rearrangements underlie globally bistable shear banding regime

Grain rearrangements govern the mechanical response of granular materials under load. A comprehensive time series analysis of macroscopic stress, previously undertaken for the persistent shear banding regime, uncovered a bistable dynamical system with two interconnected attractor basins—one tied to jamming, the other to unjamming. Here we examine the state space of local fabric of a 3D granular material to uncover the underlying grain rearrangements which induce the system to switch basins and manifest macroscopic quasistationary dynamics. The fabric state space comprises metastable attractors organized according to structural determinacy: hypostatic, isostatic and hyperstatic. Although trajectories overwhelmingly favor identity transitions which preserve local fabric, rare nonidentity transitions hold the key to basin switching. Jamming basin dynamics is governed by force chain transitions in the hyperstatic region: here redundant constraints enable force reconfigurations with little to no change in the local fabric. But as force chains become overloaded, they buckle. Buckling and attendant dilatancy push grains to the isostatic region. This in turn triggers unjamming and ensuant transitions to the hypostatic region where rattlers, though few, dominate dynamics. Rattlers provide wedge-like supports to unstable misaligned particle columns, promoting force chain formation and return to the hyperstatic region. The lateral reinforcement of an isostatically constrained grain in a trimer by the addition of a contact and/or a 3-cycle is the most probable nonidentity transition during nascent force chain evolution.

Fabric evolution and dilatancy within anisotropic critical state theory guided and validated by DEM

Fabric, expressed by means of an evolving deviatoric fabric tensor F, plays a very important role in the anisotropic mechanical response of granular materials. The Anisotropic Critical State Theory (ACST) addresses fabric anisotropy by rendering dilatancy a function of F, in addition to other state variables. In this paper, 3D DEM is used to guide the specific grain-level definition of F, the formulation of its continuum evolution equation and its effect on anisotropic dilatancy within ACST. DEM provides stress-ratio and shear strain variations as input for ACST analytical calculations of evolving fabric tensor and dilatancy, which are then favourably compared with totally independent direct measurements of these quantities by DEM. Dilatancy is shown to be strongly affected by the contact normal-based fabric tensor Fc, whose evolution is best described by a continuum equation within ACST that includes dilatancy and a quantity related to particle orientation-based fabric tensor Fp. The aforementioned favourable comparison of the results for fabric tensor and dilatancy obtained independently by ACST and DEM, confirms the validity of the core framework of ACST irrespective of any constitutive model that addresses the deviatoric stress-strain relations.