Behavior Of Granular Materials Research Articles

Optimization of Discrete Element Method Model to Obtain Stable and Reliable Numerical Results of Mechanical Response of Granular Materials

The discrete element method (DEM) is largely used to simulate the geotechnical behavior of granular materials. However, numerical modeling with this type of code is expensive and time consuming, especially when fine particles are involved. This leads researchers to make use of different approaches to shorten the time of calculation without verifying the stability and reliability of numerical results, even though a compromise between the time of calculation and accuracy is commonly claimed. The particle size distribution (PSD) curve of studied granular material is completely ignored or arbitrarily cut. It is unclear if the ensued numerical results are still representative of the studied granular materials. Additionally, one can see a large number of numerical models established on a basis of calibration by ignoring the physical meaning and even measured values of some model parameters. The representativeness and reliability of the obtained numerical results are questionable. All these partly contribute to reducing the public’s confidence in numerical modeling. In this study, a methodology is illustrated to obtain an optimal DEM model, which minimizes the time of calculation and ensures stable and reliable numerical results for the mechanical behavior of a waste rock. The results indicate that the PSD curve of the studied waste rock can indeed be cut by excluding a portion of fine particles, while the Young’s modulus of the waste rock particles can also be decreased to accelerate the numerical calculations. A physical explanation of why the time of calculation can be shortened by reducing the Young’s modulus of waste rock particles is provided for the first time. Overall, the PSD cut, reduction in Young’s modulus, and time step must be determined through sensitivity analyses to ensure stable and reliable results with the shortest time of calculation. In addition, it is important to minimize the number of model parameters determined through the process of calibration, especially for those having physical meanings. In this study, the only model parameter having a clear physical meaning but difficult to measure is the rolling resistance coefficient for repose angle tests on the studied waste rock. Its value has to be obtained through a process of calibration against some experimental results. The validity and predictability of the calibrated numerical model have been successfully verified against additional experimental results.

Biomass Moving Bed Combustion Analysis via Two-Way Coupling of Solid–Fluid Interactions Using Discrete Element Method and Computational Fluid Dynamics Method

Nowadays, almost all countries in the world are intensifying their search for locally available energy sources to become independent of external supplies. The production of alternative fuels from biomass and waste by thermal treatment or direct use in the combustion process is still the simplest method for fast and cheap heat production. However, the different characteristics of these fuels can cause problems in the operation of the plants, resulting in increased air pollution. Therefore, the analysis of the thermal treatment of solid fuels is still an important issue from a practical point of view. This work aimed to study biomass combustion in a small-scale reactor using the in-house Extended DEM (XDEM) method based on mixed Lagrangian–Eulerian approaches. This was provided by a novel, independently developed coupling computational interface. This interface allows for a seamless integration between CFD and DEM, improving computational efficiency and accuracy. In addition, significant advances have been made in the underlying physical models. Within the DEM framework, each particle undergoes the thermochemical processes, allowing for the prediction of its shape and structural changes during heating. Together, these changes contribute to a more robust and reliable simulation tool capable of providing detailed insights into complex multi-phase flows and granular material behavior. Numerical results were obtained for a non-typical geometry to check the influence of the walls on the distribution of the parameters in the reactor. The results show that XDEM is a very good tool for predicting the phenomena during the thermal treatment of solid fuels. In particular, it provides information about all the moving particles undergoing chemical reactions, which is very difficult to obtain from measurements.

Numerical model for solid-like and fluid-like behavior of granular flows

AbstractWe propose a constitutive model for both the solid-like and fluid-like behavior of granular materials by decomposing the stress tensor into quasi-static and collisional components. A hypoplastic model is adopted for the solid-like behavior in the quasi-static regime, while the viscous and dilatant behavior in the fluid-like regime is represented by a modified $$\mu (I)$$ μ ( I ) rheology model. This model effectively captures the transition between solid-like and fluid-like flows. Performance and validation of the proposed model are demonstrated through numerical simulations of element tests.

Analyzing the mechanical behavior of granular materials: A multi-morphological approach using spherical harmonics and LS-DEM

This paper investigates the micro-to-macro response of granular materials influenced by multi-scale morphological characteristics using spherical harmonics and LS-DEM. Our simulation results reveal that particle elongation plays the primary role in governing the shear strength and dilatancy, with surface roughness also affecting these macroscopic behaviors of non-elongated assemblies while marginally influencing elongated assemblies. At the microscale, more elongated particles with a higher degree of roughness present a stronger interlocking effect. Furthermore, we quantitatively establish a connection with the system stress ratio through the stress-fabric-force (SFF) relationship, enabling us to comprehend the shape-dependent macroscopic shear strength from microscopic anisotropy perspectives. Our results indicate that more elongated and rougher particles lead to a more significant fabric anisotropy at the critical state. Additionally, a mechanics-based shape parameter, known as rotational resistance angle, is found to correlate linearly with the critical shear strength of all explored assemblies, which can be explained by the microscopic linkage between all partitioned anisotropy components and the adopted shape parameter.

Deep learning-based analysis of true triaxial DEM simulations: Role of fabric and particle aspect ratio

This study investigates the influence of micro-scale entities such as inherent and induced fabric anisotropy on the stress–strain behaviour of granular assemblies. In tandem with this exploration, our objective is to formulate a novel correlation that quantifies the evolution of fabric tensor across diverse loading paths. This correlation can be introduced to enhance the micro-mechanical insights in conventional constitutive models. Employing the Discrete Element Method (DEM), we simulate the drained and undrained responses of 680 transversely isotropic particulate assemblies with diverse initial fabrics and particle Aspect Ratio (AR) under true triaxial loading conditions. We consider a second-order fabric tensor based on inter-particle contact orientations to trace fabric evolution during loading. To account for fluid–solid interaction under undrained conditions, we adopted the DEM-Coupled Fluid Method (CFM). The simulation results highlight the significant influence of the Lode angle, particle shape and initial fabric on the stress–strain behaviour of granular materials, with fabric evolution primarily affected by the stress state, void ratio and particle AR. Lastly, we propose a new correlation for the quantification of the fabric tensor using a multi-layer feed-forward neural network. The satisfactory performance of the suggested correlation is demonstrated through a comparison between DEM data and predicted fabric tensor values.

Assessing particle crushing mechanism and optimizing design for recycled aggregates in road bases via a novel particle crushing DEM method

This study introduced an innovative and effective algorithm that aims to provide a comprehensive simulation of particle crushing behavior in complex granular materials. Based on the Griffith's strength theory, the algorithm was formulated and implemented using the discrete element method (DEM). This algorithm accurately simulates the crushing behavior of real particles under arbitrary three-dimensional stress states. The robustness of the proposed method and the distribution pattern of the resulting child particles were verified through a series of single- and multi-particle crush tests. The findings demonstrate that the proposed approach exhibits exceptional generalizability, effectively describes the particle crushing behavior of granular materials, and features high efficiency and cost-effectiveness. The particle crushing simulations were conducted accordingly via DEM on a combination of natural gravel (NG), recycled mortar (RM), and recycled brick (RB) aggregates for use in road bases. The results revealed the particle crushing mechanisms in single-, binary-, and ternary-type recycled aggregate mixtures. Additionally, this study revealed the influence of recycled aggregate types on particle crushing within these different mixtures. The ternary design charts and tables were developed to determine the maximum contents of recycled aggregates in accordance with the particle crushing value requirements for different highway classes and aggregate base types. This study not only holds significant theoretical importance in developing efficient particle-crushing algorithms, but also offers valuable insights and scientific references for improving the resourceful utilization of recycled aggregates derived from construction and demolition wastes in road bases.

Hypoplastic model for solid-like and fluid-like granular flows

We present a unified constitutive model for the solid-like and fluid-like behaviour of granular materials by decomposing the stress rate tensor into frictional and collisional parts. An enhancement to the classical hypoplastic model is implemented to consider the acceleration effect in both steady and unsteady granular flows, achieved by introducing a higher-order strain rate. This model can effectively capture the rate-independent and rate-dependent behaviours observed in solid-like and fluid-like granular flows. Performance and validation of the unified model are presented through numerical simulations of diverse element tests.

Simhypo-sand: a simple hypoplastic model for granular materials and SPH implementation

This paper introduces a new hypoplastic model characterized by a simple and elegant formulation. It requires only 7 material parameters to depict salient mechanical behaviors of granular materials. The numerical implementation employs an explicit integration method, enhanced by a best-fit stress correction algorithm in a smoothed particle hydrodynamics code. The performance of this model in capturing soil behavior across a range of scenarios is demonstrated by conducting various numerical tests, including triaxial and simple shear at low strain rates, as well as granular collapse, rigid penetration and landslide process at high strain rates.

Mechanical effects of nanomaterials on the residual shear strength of dry sandy mixtures: Implication for the high mobility of rock avalanches

Nanoparticles found in rock avalanches and natural faults were inferred to be the reason for the ultra-low shear resistance of the materials along the shear surface. Nevertheless, this inference has not been physically verified yet. To investigate the role of nanoparticles in the shear behavior of granular materials, we conducted a series of ring shear tests on silicon dioxide nanoparticles (SN), silica sand (S8), and mixtures of the S8 with different contents of SN, under varying normal stresses (σ) and shear velocities (V). Our results showed that the shear strength (μ) of SN is high when σ is small (≤ 215 kPa at our test range), even though the maximum shear velocity is about 210 cm/s, but shows a great decrease under higher σ (≥ 619 kPa). The shear strength of mixtures varied with SN content. For S8 (M0) and the mixture of 10% SN (M10), when sheared under small σ, μ first decreased slightly with increasing V when V is smaller than 1 cm/s, after that it increased slightly with further increase of V. Nevertheless, this kind of shear-rate dependent behavior was not observed in the tests under higher σ. When the content of SN in the mixture was <20%, μ increased with the increase of SN content. However, with further increase of SN content, μ decreased. Under high normal stress conditions, distinctive powder rolls were observed on the shear surface formed on the tests. When the mixtures with lower SN content (≤50%), the powder rolls were not observed. We inferred that powder rolls can be produced under high SN content and high normal stress conditions, and this structure altered the particle movement mode from sliding friction to rolling resistance, resulting in a significant decrease in the shear strength. These findings provide valuable insights into the shear behavior of granular materials with nanoparticles and then provide evidence for a better understanding of the high mobility of rock avalanches.

Micromechanics of contact-bound cohesive granular materials in confined compression.

The mechanical behavior of granular materials results from interparticle interactions, which are predominantly frictional. With the presence of even very small amounts of cohesion this frictional interparticle behavior significantly changes. In this study, we introduce trace amounts of cohesive binder between the intergranular contacts in a sample of quartz particles and apply one-dimensional (1D) compression loading. X-ray computed tomography is performed in situ during 1D compression. We make observations at three different length scales. At the macroscopic or ensemble scale, we track the evolution of the porosity, particle size and the stress-strain response during this compression. At the microstructure or interparticle scale, we compute the directional distribution of contacts and the particles. We also track the evolution of the fabric chains with continued compression. We also evaluate particle rotations, displacements, contact twist, rotation, and sliding. We show through our experiments that even a small amount of cohesion (as low as 1% by weight) significantly changes the response at multiple length scales. This interparticle cohesion suppresses the fragmentation of grains, alters force transmission and changes the structure of the ensemble.

Macro and microscopic analysis of granular flow in curved hoppers

The geometry of vessels has a significant influence on granular flow. In this study, discrete element method is used to simulate the flow behavior of granular materials in curved hoppers. The results confirm that curved hoppers can achieve a higher discharge rate than conical hoppers, accompanying with a large converging flow region. The macro and microscopic characteristics such as flow and force structures are analysed in detail, revealing that the hopper curves causes the preferred flow direction of granular materials to the central region and the converging flow near the orifice is more developed, leading a higher particle velocity. The observation of flow patterns developed in hoppers shows that the affected region by the curves only occurs at the bottom, and the transition height from the mass flow to the converging flow increases with the curves deviating from the conical.

Correlation of fabric parameters and characteristic features of granular material behaviour in DEM in constitutive modelling

AbstractThe anisotropic microstructure of granular materials has a profound effect on their macroscopic behaviour and can be characterised using a fabric tensor. To include of fabric in the critical state theory (CST), anisotropic critical state theory (ACST) was proposed by modifying the state parameter $$(\psi )$$ ( ψ ) of CST to a fabric-dependent dilatancy state parameter $$(\upzeta )$$ ( ζ ) . Noteworthy that $$\uppsi$$ ψ showed a very strong correlation with characteristic features (e.g. instability, phase transformation and characteristic state) of macroscopic behaviour and, as a result, it has been adopted in many constitutive models. While $$\upzeta$$ ζ aided the inclusion of fabric in ACST models, the correlation between $$\upzeta$$ ζ and characteristic features has not been evaluated in detail yet, although a large number of works are found on micromechanics and fabric only. In this study, a large number of discrete element method simulations for drained and undrained triaxial were conducted to evaluate the correlation between $$\upzeta$$ ζ and characteristic features. To this purpose, the correlation between stress ratio and both classic and dilatancy state parameter ($$\psi$$ ψ and $$\upzeta$$ ζ ) were studied in important characteristic features (e.g. instability, phase transformation and characteristic state). It was found that this correlation was improved using $$\upzeta$$ ζ which might be due to the inclusion of fabric in our model. This observation is new and significant for inclusion of fabric evolution in constitutive modelling.

Shear rate dependency on flowing granular biomass material

The commercialization of bioenergy has been significantly limited by various material handling issues due to the poor flowability of granular biomass materials. Addressing these issues demands a fundamental understanding of flow physics and robust models to predict the multi-regime flow behavior of biomass particles. In this study, we investigated the multi-regime flow behavior of loblolly pine chips, a widely used bioenergy feedstock, through combined experiments and simulations. A quasi-static hypoplastic model and a cross-regime Drucker–Prager (DP)-μ(I) model were utilized and validated against inclined plane flow experiments to understand the quasi-static and dense flow behavior of milled pine chips. The results show that along the inclined plane, loblolly pine chips mainly present in heap flow (varying thickness along the plane), and in plane flow (iso-thickness along the plane) only when the inclination closes to the material’s critical state internal friction angle. The results also show that the multi-regime DP-μ(I) model predicts a completely different velocity profile from the hypoplastic model. DP-μ(I) model can capture the flow behavior of pine chips in both flow regimes well but at the cost of extra parameter determination, and the shear-rate dependent rheology model can successfully capture the flow of elongated high-frictional particles. These findings advance the scientific understanding of the multi-regime flow behavior of granular biomass materials and shed light on formulating novel constitutive models to assist granular biomass handling in the bioenergy industry.

Micromechanics of multiphase geomaterials based on micro-CT image analysis: unsaturated soil, vegetated soil, and bio-cementation

Under the influence of climate change, extreme weather events such as rainstorms may induce fluctuations in soil water content above the groundwater level, thereby causing geological disasters (e.g., landslides). To mitigate these hazards, green and low-carbon engineering measures such as vegetation reinforcement and bio-cementation are proposed. This study investigates the micromechanical properties of multiphase geomaterials—unsaturated soil, vegetation-reinforced sand, and bio-cemented sand—utilizing high-resolution computed tomography (CT) scanning technology and associated image analysis techniques. The findings are presented as follows: (1) a 4D examination of the macroscopic and microscopic behaviors of unsaturated granular materials under triaxial loading conditions was conducted using self-designed in situ CT scanning equipment. (2) Triaxial loading alters the distribution of phase interfacial surfaces in unsaturated soil, affecting its overall strength. This loading also increases the anisotropy of the solid skeleton and suction stress. (3) The global saturation of the root–soil complex diminishes with root growth, with pore distribution significantly influencing local saturation. (4) In the unsaturated MICP process, low-saturation conditions are preferable for effective cementation, although the saturation levels should be restricted to 20%. After calcification, the particle contact coordination number increases, maintaining the isotropy in the contact between the soil particles.

Effect of gravity on granular material flows

Most geohazards and industrial processes are essentially gravity-driven dense granular flows. Deep understanding of the effect of gravity on granular flow is of crucial importance in analyzing the evolution of planetary surfaces. By using a discrete element numerical simulation method, we obtain the evolutionary characteristics of velocity, volume fraction, shear rate and granular temperature during granular flow, and analyze the effect of gravity on the rheological behavior of granular materials. The results indicate that gravity significantly affects the flow characteristics of granular materials, especially in the case of large inclination angle. With the increase of gravity, the flow velocity, shear rate and granular temperature of the granular material tend to increase. When the inclination angle exceeds the critical value, the volume fraction of the granular system in the high gravity environment decreases significantly, while the inertia number increases.

Variability and loss of uniqueness of numerical solutions in FEM×DEM modeling with second gradient enhancement

AbstractIn the last decade, a new multi‐scale FEM×DEM approach has been developed using Finite Element Method (FEM) coupled with Discrete Element Method (DEM) as a constitutive law to account for the specificities of the mechanical behavior of granular materials. In FEM×DEM model, a DEM calculation is performed on a particle assembly (volume element—VE) at each Gauss point. Recent publications have demonstrated that FEM×DEM approach naturally captures the discrete and anisotropic nature of granular materials. Despite its advantages, FEM×DEM with classical FEM, suffers from mesh dependency, especially when material enters softening phase and exhibits strain localization. To overcome this limitation, FEM×DEM model has been enriched by incorporating a local second gradient model. Nevertheless, the existence of multiple possible solutions is observed. In this paper, we study the variability and loss of uniqueness of numerical solutions to a boundary value problem. Different VEs with equivalent mechanical properties are generated and used to model the pressuremeter tests by means of FEM×DEM. The modeling results show a great variability of the numerical results, both in shape of borehole and in different modes of shear bands. For the same VE, the loss of uniqueness of numerical solutions is evidenced by a slight modification of loading history at the level of the internal pressure applied to the borehole. Finally, we show that when a certain heterogeneity is introduced by using different VEs within the same BVP, even if the uniqueness of the solution is not guaranteed, the set of possible solutions seems more restrained.

A pressure-sensitive rheological origin of high friction angles of granular matter observed in NASA–MGM project

Abstract An abnormally high peak friction angle of Ottawa sand was observed in (National Aeronautics and Space Administration) NASA–(Mechanics of Granular Materials) MGM tests in microgravity conditions on the space shuttle. Previous investigations have been unsuccessful in providing a constitutive insight into this behavior of granular materials under extremely low effective stress conditions. Here, a recently proposed unified constitutive model for transient rheological behavior of sand and other granular materials is adopted for the analytical assessment of high peak friction angles. For the first time, this long-eluded behavior of sand is attributed to a hidden rheological transition mechanism, that is not only rate-sensitive, but also pressure-sensitive. The NASA–MGM microgravity conditions show that shear-tests of sand can be performed under abnormally low confining stress conditions. The pressure-sensitive behavior of granular shearing that is previously ignored is studied based on the μ(I) rheology and its variations. Comparisons between the model and the NASA microgravity tests demonstrate a high degree of agreement. The research is highly valid for pressure-sensitive and rate-dependent problems that occur during earthquakes, landslides, and space exploration.

3D DEM-based particle-scale analysis of drained and undrained triaxial behaviors of granular materials

3D DEM-based particle-scale analysis of drained and undrained triaxial behaviors of granular materials

High-cycle shakedown, ratcheting and liquefaction behavior of anisotropic granular material with fabric evolution: Experiments and constitutive modelling

Although the mechanical response of granular materials strongly depends on the interplay between their anisotropic internal structure (fabric) and loading direction, such coupling is not explicitly considered in existing high-cycle experimental datasets and models. High-cycle experiments on granular specimens specifically prepared with various fabric orientations are presented. It is found that the high-cycle strain accumulation behavior can change remarkably, from shakedown to ratcheting, when the fabric orientation deviates more from the loading direction. Inspired by the experimental observations, a fabric-dependent anisotropic high-cycle model is proposed, by proper recasting of an existing model formulated within Critical State Theory, into the framework of Anisotropic Critical State Theory. The model explicitly accounts for the fabric evolution, which is linked to plastic modulus, dilatancy and kinematic hardening rules. The model can quantitatively reproduce the high-cycle strain accumulation (i.e., shakedown and ratcheting) under drained conditions, as well as pre-liquefaction and post-liquefaction responses granular materials having widely ranged fabric anisotropy, densities and cyclic loading types using a unified set of constants. It exhibits a unique feature of simulating the distinct high-cycle strain accumulation and liquefaction of granular material with various fabric anisotropy, while the existing high-cycle models treat them equally. The successful reproduction of the anisotropic sand element response under high-cycle drained and undrained conditions makes it possible to perform whole life analysis of various foundations on granular soil subjected to high-cycle loading events.

Systematic investigation into the role of particle multi-level morphology in determining the shear behavior of granular materials via DEM simulation

This study aims to numerically investigate the dependence of shear behaviors of granular materials on particle multi-level morphology, encompassing form (mean of elongation and flatness), angularity, and roughness. To this end, four series of particles—ellipsoidal particles with varying elongation indices (EI) and flatness indices (FI), and equiaxed concave particles with varying angularity indices (AI) and roughness (RG)—are adopted to isolate the effects of particle morphology at each level. Through discrete element method (DEM) simulations, granular assemblies with varying values of EI, FI, AI, and RG are consolidated to achieve the maximum packing density under the same confining pressure. Subsequently, they are subjected to triaxial drained compression tests until reaching a critical state. Based on numerical results, the independent effects of EI, FI, AI, and RG on the macro- and micro-mechanical response of granular materials are examined and compared in detail. Furthermore, using the ‘Stress-force-fabric’ (SFF) relationship, the anisotropic origins of the peak- and critical-state shear strengths induced by EI, FI, AI, and RG are also analyzed.