Response Of Granular Materials Research Articles

Macro-micro mechanical study of principal stress rotation in granular materials using DEM simulations of hollow cylinder test

The dependency of sand behavior anisotropy on microstructure reveals the importance of macro-micro mechanical analysis of the principal stresses rotation effect on the strength-deformation response of granular material. In this study multi-scale analysis of the granular material's behavior using three-dimensional discrete element method simulations of the hollow cylinder test was presented. The effect of principal stresses rotation (α) on the macro-mechanical behavior of the soil was investigated from the micro-mechanical anisotropy aspect. It was observed that principal stress rotation affects the anisotropy coefficient and directional distribution of all micro-parameters which can change the soil's behavior according to loading conditions. The stress-force-fabric relationship was used to analyze the microstructure's stress state based on micro-parameters anisotropy coefficients. In addition to the good agreement between stress-force-fabric and general stress tensors, the decreasing trend of the maximum deviator stress and internal friction coefficient angle with increasing α can be observed for both stress tensors.

Quantifying fabric anisotropy of granular materials using wave velocity anisotropy: a numerical investigation

Fabric anisotropy is a sought-after micro index to correlate macro mechanical responses of granular materials. In this work, the discrete-element method is utilised to simulate multi-directional bender element tests in granular soils to obtain the evolution of wave velocities during drained conventional triaxial (CT) and true triaxial (TT) tests; the contact normal-based fabric is simultaneously monitored for bridging the fabric anisotropy and wave velocity anisotropy. The results show that stress-normalised wave velocities and microscopic fabric, including contact normal distribution and coordination number, remain nearly constant until a stress ratio threshold is reached. After the threshold value is reached, stress-normalised wave velocities start to decrease, especially in the minor principal stress direction, accompanied by significant adjustment of coordination number and fabric anisotropy. The results also reveal that the normalised wave velocity depends on the contact normal densities in the wave propagation and particle oscillation directions. With the contact normal distribution represented by a density function, a good linear relationship between the microscopic fabric anisotropy and macroscopic wave velocity anisotropy is obtained for both CT and TT tests.

Linking the macro-scale response of granular materials during drained cyclic loading to the evolution of micro-structure, contact network and energy components

This study has considered the behaviour of granular materials subjected to drained cyclic loading under constant mean effective stress. Using the discrete element method, cubical, isotropically compressed samples were subjected to 50 loading cycles at different values of mean stress (p' = 100, 200, 300 kPa) and different loading amplitudes (zeta = 5%, 10% and 20% of p'). At low cycle numbers, the deformation mechanism is controlled by contractive volumetric strains, before transitioning to the ratcheting regime, characterised by the persistent accumulation of plastic strains. An energy/work analysis showed that the volumetric work per cycle decreased as hysteresis loops tighten. During ratcheting, most boundary work was dissipated by contact sliding. The mechanical response was controlled by zeta, with little to no influence of p'. For zeta = 5%, deformations were confined to the elastic range, with no increase in secant stiffness G_{sec} or shear strength after cyclic loading. For zeta = 10%, G_{sec} and the shear strength increased after cyclic loading, although no significant expansion of the yield surfaces was observed. The largest loading amplitude (zeta = 20%) induced yielding at low cycles, leading to significant changes in the fabric, volume and yield surfaces of the samples, and a significant increase of shear strength and G_{sec}. At the micro-scale, graph theory was used to quantify the evolution of the contact network. After sim 20 loading cycles, the network reached a steady-state of constant but persistent topology changes in the material, with most of the topology retained between loading cycles.

Spatial clustering of microscopic dynamics governs the slip avalanche of sheared granular materials

Establishing quantifiable links between individual-particle dynamics and macroscopic response of granular materials has been a longstanding challenge, with implications in material science, geology and industry. Despite sustained efforts in uncovering generic features in both macroscopic flow and microscopic dynamics, further advance on the subject matter demands quantitative correlations to be established. We propose a 3D convolution neural network (CNN) to quantify the link between microscopic dynamics and macroscopic stress fluctuations, including both stress recharge (stick regime) and stress drop (slip regime). Through the model interpretation, microscopic dynamics is found to demonstrate distinctive spatial patterns in the stick and slip regimes, which root in the result of free volume-induced structural rearrangements and contact network dynamics, respectively. We conclude that the spatial clustering of microscopic dynamics governs the occurrence of slip avalanches and acts as the “fingerprint” of macroscopic stress fluctuation. The data-driven framework developed in this paper can be readily extended to other amorphous solids for building cross-scale relations, paving a new way to understand the complex behavior of amorphous solids.

Experimental study on horizontal pressure of column-supported concrete group silos under earthquake force

ABSTRACT The overpressure of silo wall caused by granular materials under earthquake is one of the main reasons of silo damage. Two shaking table model tests were carried out with column supported silos and independent single silos, respectively. The seismic response of silo granular materials was analyzed first, and then the dynamic lateral pressure of silo wall under different levels of earthquake and overpressure coefficient were obtained. The results showed that the interaction between the granular materials and the silo wall in the group silos is related to the position of the individual silo. The seismic response of granular materials is linked with the spectral characteristics of seismic waves. The overpressure coefficients of the corner silo and the side silo are greater than that of the independent single silo with a 7% and 9% higher value, respectively. Apparently, the seismic response characteristics of the independent single silo are totally different from that of the group silos. It was concluded that when designing the wall of the group bin, the position of the bin should also be considered.

Relationship between acoustic emission and energy dissipation: a DEM study of soil–structure interaction

Acoustic emission (AE) monitoring offers the potential to sense particle-scale interactions that lead to macro-scale responses of granular materials; however, there remains a paucity of understanding of the fundamental links between particle-scale mechanisms and AE generation in particulate materials, which limits interpretation of the measured AE. The objective of this study was to establish links between particulate-scale energies and AE activity measured at the macro-scale in experiments. To achieve this, a programme of 3D DEM simulations was performed on granular soil/steel structure interfaces and the results were compared with experimental measurements. The findings show that the fundamental particulate-scale mechanisms that contribute to AE generation are friction and damping in particulate rearrangement, with friction being the dominant mechanism (i.e. > 95% of the total energy). Dissipated plastic energy was influenced in the same way as measured AE activity by unload–reload behaviour, imposed stress level, mobilised shearing resistance, and shearing velocity. Relationships have been established between AE and dissipated plastic energy (R2 from 0.96 to 0.99), which show AE generated per Joule of dissipated plastic energy is significantly greater in shearing than compression. A general expression has been proposed that links AE and plastic energy dissipation. This new knowledge enables improved interpretation of AE measurements and underpins the development of theoretical and numerical approaches to model and predict AE behaviour in particulate materials.

Contact Overlap Calculation Algorithms and Benchmarks Based on Blocky Discrete-Element Method

The mechanical response of granular materials has been investigated widely using discontinuous modeling, such as the discrete-element method (DEM). Contact detection and contact resolution have been critical issues when modeling multiple body contacts, especially for arbitrary polyhedral blocks. In this study, the contact overlap calculation algorithms, including polyhedron–polyhedron and polyhedron–boundary contact, were developed to calculate the contact characteristics. For polyhedron–polyhedron contact, the contact overlap volume algorithm is developed based on the geometric dualization theory. The Gilbert–Johnson–Keerthi (GJK) and Quickhull algorithms are used to calculate the overlap polyhedron. The contact characteristics, such as normal direction (n), contact area (a), and penetration depth (un) could be extracted from the contact overlap volume. For polyhedron–boundary contact, a novel and effective algorithm is presented, where the polyhedron–boundary contact is transformed into polyhedron–triangle contact. Then, two types of benchmarks are used to verify the previously mentioned algorithms, which demonstrated that the algorithms could handle the complicated contact types and maintained contact continuity even from face to edge contact. As a complex benchmark, the failure process in a masonry structure is simulated and compared with the model test.

Data-driven strain–stress modelling of granular materials via temporal convolution neural network

Machine learning offers a new approach to predicting the path-dependent stress–strain response of granular materials. Recent studies show that temporal convolution neural (TCN) networks, a mutation of the 1D convolution neural network (CNN), have a powerful capability of addressing time-related prediction tasks. In this work, TCN networks are constructed to explore their potential in capturing the constitutive law of granular materials. To train and test the TCN network, three types of numerical experiments are implemented to generate datasets via discrete element modelling. The Bayesian optimisation method is employed to find the optimum architecture of the network. Furthermore, to improve the training accuracy and efficiency, a transfer learning (TL) scheme is innovatively leveraged, which utilises the trained network parameters from a set of shorter time steps and/or coarser data points of the training strain–stress loading curves, as the initial values, to train the network for a longer time step. The prediction ability of the trained TCN network is assessed and compared with a recurrent neural network which has been proved to perform well in predicting constitutive laws of the granular materials. In addition, training datasets with artificially added noise are also used to test and analyse the robustness of TCN networks.

Linking inherent anisotropy with liquefaction phenomena of granular materials by means of DEM analysis

The liquefaction phenomena of sands have been studied by many researchers to date. Laboratory element tests have revealed key factors that govern liquefaction phenomena, such as relative density, particle size distribution, and grain shape. However, challenges remain in quantifying inherent anisotropy and in evaluating its impact on liquefaction phenomena. This contribution explores the effect of inherent anisotropy on the mechanical response of granular materials using the discrete element method. Samples composed of spherical particles are prepared which have approximately the same void ratio and mean coordination number (CN), but varying degrees of inherent anisotropy in terms of contact normals. Their mechanical responses are compared under drained and undrained triaxial monotonic loading as well as under undrained cyclic loading. The simulation results reveal that cyclic instability followed by liquefaction can be observed for loose samples having a large degree of inherent anisotropy. Since a sample having initial anisotropy tends to deform more in its weaker direction, leading to lower liquefaction resistance, a sample having an isotropic fabric potentially exhibits the greatest liquefaction resistance. Moreover, the effective stress path during undrained cyclic loading is found to follow the instability and failure lines observed for static liquefaction under undrained monotonic loading. From a micromechanical perspective, the recovery of effective stress during liquefaction can be observed when a threshold CN develops along with the evolving induced anisotropy. Realising that the conventional index of the anisotropic degree (a) is not effective when the CN drops to almost zero during cyclic liquefaction, this contribution proposes an alternative index, effective anisotropy (a×CN), with which the evolution of induced anisotropy can be tracked effectively, and common upper and lower bounds can be defined for both undrained monotonic and cyclic loading tests.

Response of granular material under combined principal stress value and orientation change in 3D space

Response of granular material under combined principal stress value and orientation change in 3D space

An Enhanced Automated Particle Angularity Measurement Method

Abstract Angularity is an important aspect of particle morphology, directly correlated to the mechanical response and strength of granular materials. Many researchers have proposed multiple direct and indirect methods such as visual charts, analytical formulas, and advanced image-based techniques for qualitative and quantitative assessment of particle angularity, but no single method has been fully successful in distinguishing all types of particles and obtaining an accurate quantitative value of angularity. Nevertheless, because of the significant importance of the parameter, researchers have been using a few generally accepted angularity quantification methods. This paper evaluates the conceptual merits and demerits of four such methods, namely, two analog methods called “roundness index” and “degree of angularity” coined by Wadell and Lees, respectively, as well as two image-based methods called “angularity using outline slope” and “gradient angularity index” proposed by Rao, Tutumluer, and Kim and Chandan et al., respectively. The latter two methods were developed for use in conjunction with the University of Illinois Aggregate Image Analyzer and the Aggregate Imaging System, respectively. A new approach for angularity quantification is proposed herein based on insights from a rigorous analysis and critical assessment of these methods. The proposed method is compared against the existing methods based on Ward’s linkage method of clustering and is shown to be superior at distinguishing between various classes of particles. The proposed approach is demonstrated to be a better measure of the sharpness of the meso-level geometrical features of importance along a particle’s outline that are the controlling parameters contributing to particle angularity, which consequently correlates to the kinematic and mechanical response of granular materials.

Explaining the Response of Granular Materials to Shear Deformation Using Statistics and Network Analysis

Explaining the Response of Granular Materials to Shear Deformation Using Statistics and Network Analysis

Rheological response of granular materials under dynamic conditions

The rheological behaviour of a dense granular bed under dynamic conditions is investigated by simulating granular flow in the FT4 powder rheometer using the Discrete Element Method. The distribution of the prevailing stresses and strain rates in the granular bed, and their dependence on material properties and blade operational conditions, are analysed. The shear stress was found to be approximately constant in the radial direction along the blade but dissipates in the circumferential direction away from the blade. Analogously, the strain rate decreases with increasing angular distance away from the blade as the bed becomes less dynamic. An increase in the blade tip speed, particle aspect ratio and interfacial energy results in an increase in the average shear stress in the granular bed. A predictive model is proposed to compute the average shear stress in the granular bed based on the blade torque by considering the effects of blade tip speed, particle aspect ratio and interfacial energy.

A simple discrete-element model for numerical studying the dynamic thermal response of granular materials

This paper aims to investigate the influence of periodicity temperature change on the properties of dry granular materials in macroscopic and microscopic. A series of cyclic thermal consolidation tests have been carried out based on the discrete element method (DEM) that incorporate particles’ volumetric thermal expansion coefficient. The simulation of the direct shear test was carried out on the samples after thermal cycling. Results showed that thermally-induced volumetric strain accumulation of the specimen can be calculated by the DEM model, based on the two-dimensional particle flow code (PFC2D) software. The lateral pressure degraded concomitantly thanks to decreases in particles’ horizontal contact during periodic thermal cycling. In addition, the shear dilatancy level decreases during the shearing process with the number of thermal cycles. Both the size and anisotropy of the normal contact force and contact number and the force chain are affected by the temperature cycle. Finally, the results of this paper have a certain reference for the engineering practice, such as thermal piles or others, when granular materials are subjected to thermal cycling.

Comparative FE-studies of interface behavior of granular Cosserat materials under constant pressure and constant volume conditions

This article shows the outcomes of a systematic series of finite element (FE) calculations relevant to the shear behavior of a particulate-continuum interface system under different normal boundary conditions. In this respect, shearing of a thin and long granular Cosserat layer in the vicinity of a rigid moving wall with varied surface roughness values is analyzed under constant normal pressure and constant volume conditions. The material behavior is defined with a special elasto-plastic Cosserat model, taking into account micro-rotation, micro-curvature, couple stress, and mean particle size. The interaction between the layer of boundary particles and the surface roughness of the adjoining bottom wall is modeled by the rotation resistance of particles along the wall surface. Herein, the coupled effects of normal confining constraints imposed on the layer and the surface roughness of the bottom wall, are considered on the response of granular material under shearing. The influences of pressure level and initial void ratio are explored as well. Numerical results demonstrate that the dilatancy constraint prescribed to the interface plane in the normal direction, and the wall roughness have visible influences on the interface shear resistance as well as the deformation field formed within the layer. After large shearing, the width of the localized zone along the wall does not necessarily depend on the normal confining constraint and the applied pressure level. However, the localized zone characteristics and the interface shear response are mainly affected by the initial void ratio of the material. In addition to FE analyses, DEM-based simulations are also performed to investigate the micro-mechanical response of granular medium adjacent to a wall under shearing. FE predictions are qualitatively compared with DEM results, and reasonable agreement is observed.

Discrete element analysis of earthquake surface fault rupture through layered media

The influence of soil inhomogeneity on earthquake surface fault rupture is analyzed using the discrete element method (DEM). Particle assemblages are produced with layers having contrasting relative density. Similar to that observed in homogenous soil simulations, loose layers tend to absorb the localized shear deformation from underlying dense layers and disperse it over a broader area. However, the rupture can re-localize as it moves into an overlying dense layer. The ground surface deformations produced by fault rupture through layered soils are bounded by the ground surface deformation produced in homogeneous soil. The presence of a thin layer does not significantly alter the path of fault rupture propagation of a steeply dipping dip-slip fault. Conversely, a loose thin layer within dense soil can divert the path of fault rupture propagation during shallow reverse fault rupture by providing a kinematically compatible path of low shear resistance. Stresses are homogenized within the simulations to highlight the capability of DEM to capture the response of granular materials in scenarios that are difficult to achieve physically in the laboratory.

CONSTITUTIVE RELATIONS OF GRANULAR MATERIALS BY INTEGRATING MICROMECHANICAL KNOWLEDGE WITH DEEP LEARNING

Constitutive relations of granular materials are of great significance to many fields, such as geotechnical engineering. Different from traditional phenomenological constitutive theory, this study explores a micromechanics-informed data-driven constitutive modelling approach for granular materials via machine learning models. On the basis of Vogit’s homogenization assumption, an analytical small-strain stress-strain relation is established. This relation uniquely determines a group of micromechanical fabric variables associated with the constitutive behavior of granular materials. These recognized variables, together with principal strain and stress sequence pairs reflecting macroscopic properties of granular materials, are obtained via a series of discrete element models of triaxial compression tests. Considering the fact that these microscopic fabric tensors are internal variables, which cannot be directly used as inputs of a material constitutive model, a directed graph is introduced to incorporate microstructural information implicitly in the prediction of stress-strain responses. The gated recurrent unit (GRU) based recurrent neural networks are used as basic deep learning models to describe the mapping relation between nodes in the designed directed graph. In this study, the entire stress-strain prediction model can be assembled with two neural networks that are trained separately, after unfolding the directed graph from the target node to the source node. By testing the trained deep learning model based on brand new datasets, the results demonstrate that the proposed training approach can satisfactorily capture the multi-directional stress-strain responses with reversal loadings, such as conventional triaxial compression with unloading-reloading cycles, true-triaxial compression with constant intermediate principal stress (constant-b), and constant mean effective effective stress (constant-p) conditions with unloading-reloading cycles. The prediction results also show that the trained model possesses satisfactory interpolation and extrapolation capability. Considering the excellent ability of deep learning in terms of capturing the mechanical responses of granular materials and the unique features of open learning when new data is available, integrating a data-driven paradigm with theoretical constitutive models may be one of the important directions for constitutive research of granular materials.

Discrete element simulations of drained granular material response under multidirectional rotational shear

Multidirectional shearing tests on soils in the laboratory suffer from drawbacks such as non-uniformity of stress and unknown horizontal stress of the specimen. As a promising numerical technique, the discrete element method (DEM) enables investigation of the responses of virtual granular samples under general loading conditions and provides ideal numerical results to overcome the aforementioned limitations. In this study, three different drained cyclic tests, including conventional rotational shear, bidirectional circular rotational shear, and bidirectional elliptical rotational shear, were conducted on both isotropic and transversely isotropic samples under various stress ratios and density conditions. In all these tests, the magnitudes of the three principal stresses were kept constant during the entire loading process. Principal stress rotation occurred in one deviatoric stress plane in a conventional rotational shearing test but spatially (not necessarily in one plane) in the other two bidirectional shearing tests. The normalized deviatoric strain increment was decomposed into (1) coaxial and proportional, (2) coaxial and orthogonal, and (3) totally non-coaxial parts in reference to the deviatoric stress tensor. Their evolutions are presented and discussed in detail herein. The internal structure quantified by the contact-normal-based fabric tensor was tracked, and its correlation with the imposed stress path is illustrated.

An Experimental Study of the Effect of Particle Shape on Force Transmission and Mobilized Strength of Granular Materials

Abstract Force chains have been regarded as an important hallmark of granular materials. Numerous studies have examined their evolution, properties, and statistics in highly idealized, often circular-shaped, granular assemblies. However, particles found in nature and handled in industries come in a wide variety of shapes. In this article, we experimentally investigate the robustness of force chains with respect to particle shape. We present a detailed analysis on the particle- to continuum-scale response of granular materials affected by particle shape, which includes the force transmission and mobilized shear strength. The effect of shape is studied by comparing experimental results collected from shear tests performed on 2D analog circular- and arbitrarily shaped granular assemblies. Particle shapes are directly discretized from X-ray CT images of a real sand sample. By inferring individual contact forces using the granular element method (GEM), we provide a direct visualization of the force network, a statistical characterization of the force transmission and a quantitative description of the shear strength in terms of rolling, sliding, and interlocking contact mechanisms. We report that force chains are less prevalent in assemblies of arbitrarily-shaped particles than in circular-shaped samples. Furthermore, interlocking is identified as the essential contact mechanism that (1) furnishes a stable structure for force chains to emerge and (2) explains the enhanced shear strength observed in the arbitrarily-shaped samples. These findings highlight the importance of accounting for particle shape to capture and predict the complex mechanical behavior of granular materials across scales.

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.