Behavior Of Granular Materials Research Articles

Capturing the random mechanical behaviour of granular materials: a comprehensive stochastic discrete-element method study

This research pioneers a stochastic discrete-element method (DEM) by integrating the probability density evolution method (PDEM), offering a novel approach to connect particle-scale property uncertainties, specifically inter-particle friction coefficient (μ) and particle shear modulus (Gp), with macro-scale soil behaviour. Through 1100 DEM simulations, this study reveals that, for uniform particle size distribution, the uncertainty in μ substantially affects large-strain soil behaviour, with its effect being associated with packing density and soil state. The uncertainty effect of μ remains pronounced at the critical state, while the packing density effect diminishes. Stress distribution appears insensitive to uncertainty of μ, rather suggesting a predominant influence of particle size distributions. In contrast, the uncertainty effect of μ becomes negligible on small-strain behaviour, demonstrating a limited effect on small-strain stiffness. Uncertainty in Gp presents limited effects on large-strain behaviour, including stress ratios and dilatancy. At small strains, Gp shows a significant impact on stiffness, diverging from minimal influence identified for μ. This study presents a framework that integrates experimental techniques to study particle-scale uncertainty propagation, enhancing predictions of macro-scale soil behaviour. This approach could be beneficial for precise multi-scale simulations, incorporating particle-level uncertainties in engineering-scale models, thereby improving geotechnical practice predictability.

Computed Tomography-Driven Analysis of Particle Breakage Using a Coupled FDM-DEM Approach

This study proposes a refined approach for simulating the mechanical behavior of soils under high stress by integrating the Finite Difference Method-Discrete Element Method (FDM-DEM) with in-situ experiment. This novel framework incorporates advanced technologies such as flexible membrane and X-ray computed tomography (CT) to enhance the predictive capabilities of the simulation with physical insight. The FDM-DEM model adeptly simulates irregular particle shapes, capturing their interactions and the dynamics of particle breakage. The use of flexible membrane within the model further enriches this approach by enabling the capture of deformation responses in granular materials during shearing. Moreover, the adoption of CT technology facilitates continuous optimization of the simulation process. Validation through in-situ experiments has confirmed the model's effectiveness. The ability of the model to predict areas of high stress concentration—and their correlation with observed particle breakage patterns—underscores the utility of the enhanced FDM-DEM framework as a robust predictive tool for understanding the behavior of granular materials under shearing.

Multiscale data-driven modeling of the thermomechanical behavior of granular media with thermal expansion effects

A multiscale data-driven (MSDD) methodology is proposed for simulating the thermomechanical behavior of granular materials subjected to thermal expansion. The macroscale is handled using a continuous model based on the Finite Volume Method (FVM), while the microscale response is captured at Representative Volume Elements (RVEs) with the Discrete Element Method (DEM). To significantly reduce the computational cost of the analyses, the microscale DEM computations are not performed online, i.e., simultaneously with the macroscale FVM ones, as generally done in standard multiscale approaches. Instead, they are performed in advance to create a comprehensive database of RVE solutions under different initial conditions and thermal strains. This dataset is then used to train an Artificial Neural Network (ANN), which serves as a surrogate model for the macroscale solver. The MSDD approach is validated against pure DEM solutions of problems with distinct thermal conditions. Remarkably, we demonstrate that with only three input parameters, namely porosity, fabric, and thermal strain, the surrogate model can predict the microstructure evolution, as well as the updated conductivity and Cauchy stress tensors of the granular assembly. This allows for a generally accurate simulation of transient thermomechanical analyses at a drastically lower computational cost than the pure DEM approach.

Numerical investigation of the fast shear behaviour of granular materials and its significance for rapid landslides

The shear behaviour of granular materials at high velocities is crucial for understanding the high mobility of rapid landslides and the low-friction mechanisms behind them. Here, a numerical ring shear model driven by granular shear platens was developed, and this model was validated in terms of the kinematics and mechanics of the granular material. The granular material was then accelerated at different accelerations to high shear velocities (ranging from 0.001 m/s to a maximum of 5.0 m/s). The results indicate that with increasing shear velocity, the shear behaviour of granular materials transitions from a single behaviour to a composite behaviour. The composite shear behaviour is important for both the shear flow state and the frictional characteristics. The velocity profile reveals the transition of granular materials from uniform shear flow to composite shear flow consisting of locally high-shear-rate layers and slow creep layers; the volume of granular materials transitions from global expansion at the onset of shearing to local expansion; and particle velocity fluctuations and contact force fluctuations change from being uniformly distributed and relatively small at the beginning of shearing to rapid growth in local areas. Furthermore, with increasing shear velocity, the frictional characteristics become nonuniform. Local areas exhibit positive velocity-related friction effects, whereas the friction of the particles in other regions slightly decreases. Particle fluctuations represent an important factor that leads to the composite shear behaviour of granular materials. This study provides valuable insights into the shear behaviour of particles in rapid landslides.

Predicting cyclic liquefaction behavior of saturated granular materials using an updated state evolution model

Liquefaction and dynamic response of granular materials under dynamic loading has been studied intensively in field and laboratory tests. However, theoretical modeling and analytical solutions on liquefaction are still lagging and investigations are mostly restricted to laboratory observations. To investigate undrained liquefaction shear deformation and fluidity of granular material, the updated state evolution model is proposed by introducing an excess pore water pressure ratio parameter. A series of undrained cyclic triaxial tests and DEM simulations are conducted to verify the proposed model. The result indicates that the liquefaction behavior of granular materials can be captured by the updated state evolution model both at constant and varying loading frequency. Furthermore, the state parameter based on the deviatoric strain and excess pore water pressure ratio is determined to quantify assess the fluidity of granular materials. It facilitates the refinement of the discriminative criteria for cyclic liquefaction of granular materials. This parameter increases slowly at the beginning of loading, followed by a rapid and fluctuating rise, and reaches the peak before the initial liquefaction. Another significant finding is that the turning point of the state parameter range from 0.89 to 0.95 in the θ−t/t0 plane and between 0.84 and 0.94 in the θ−ru plane, as affected by the cyclic loading conditions.

Mechanical behaviour of granular materials undergoing grain dissolution

Geotechnical engineering projects are often at risk from threats related to mineral dissolution and loss of particles that constitute the matrix of the geomaterial. Moreover, the impact of climate change can exacerbate these risks by accelerating the physical processes. To address such challenges, it is a pre-requisite to understand and quantify the effect of mineral dissolution on geomechanical behaviour. A general theoretical approach to mechanical consequences of geomaterials experiencing mineral dissolution was first proposed. Following, a series of oedometer tests were conducted using mixtures of salt and sand with various salt contents to observe and characterise the effect of dissolution on the mechanical behaviour of granular materials. The dissolution of salt crystals was performed in three different stress states to observe the stress-dependent response of the material. The effect of dissolution was dependent both on the amount of dissolved salt particles and the applied stress state. The laboratory experiments and the discussion followed shares insights into the effect of grain dissolution on the mechanical behaviour of granular materials and proved the potential of the framework presented in this paper. Finally, the paper ends by discussing the engineering implications bearing in mind the climate change we are facing today.

The effect of projectile nose shape on the formation and expansion of impact-induced ejecta for sand target

Understanding the ejecting behavior of granular materials under impact conditions is of vital important for the asteroid sampling and defense. During the impact and penetration stages, the interaction between the projectile and the target controls the impact-induced ejecta behavior. However, the correlation between projectile nose shape and the formation and expansion characteristics of the ejecta remains unclear. In this study, a vertical launch system and high-speed camera were used to carry out the experiments of projectile impact on sand target at 100 m/s. The variations of ejecta parameters induced by different projectile shapes (cone and ogive) and sharpness (cone angles of 30°, 60°, 120°; Caliber-Radius-Head values of 0.5, 1.0, 3.0) were compared. The results showed that both the formation and expansion of the ejecta are influenced by the projectile shape, especially the sharpness of projectile nose. Ejecta parameters such as the emergence time, horizontal expansion velocity, and ejecta mass are positively correlated with the sharpness of projectile nose, while emergence diameter and ejecta angle exhibit a negative correlation. The above observed phenomena are attributed to the energy deposition rate of the projectile on the target during the impact stage and the flow direction of sand grains after the projectile-grain interaction during the penetration stage. These findings can gain an insight into the influence of projectile shape on the ejecting behavior of granular materials. In addition, these findings offer valuable references for the modification of ejecta models that incorporate projectile nose shapes and contribute to the design of impact sampling mechanisms in practical tasks.

Strength and fabric anisotropy of granular materials under true triaxial configurations using DEM

This paper investigates the strength and fabric anisotropy of granular materials under true triaxial configurations using the discrete element method. A clump logic based on the multi-sphere approach was utilized to replicate realistic particle shapes. The evolutions of deviatoric stress and volumetric strains were found to be independent of mean effective stress, and intermediate principal stress parameter (b). From a macroscopic viewpoint, all samples exhibited initial strain hardening followed by softening behaviour, stabilizing at large deviatoric strains due to the dense state of assemblies. The peak state friction angles showed dependency on the b-value, aligning closely with experimental findings. Microscopic parameters such as mechanical coordination number and sliding fraction were found to be approximately independent of b-values. Additionally, non-coaxiality was observed for various b-values except for specific shear modes, aligning with previous findings using spherical particles. These results highlight the capability of clumped particles to simulate the true mechanical behaviour of granular materials and contribute to our understanding of their complex response under different loading conditions.

Tracking the movement of quartz sand particles with neural networks

Tracking the movement of particles is of paramount significance for studying the impact of particle breakage on the macroscopic mechanical behaviour of granular materials and remains a persistent challenge to date. This paper presents a novel particle tracking method that integrates Pointon and PointNetLK networks, enabling an accurate tracking of both intact and broken Leighton Buzzard sand (LBS) particles. Initially, morphological information of LBS particles was extracted from X-ray micro-tomography (CT) data collected from a miniature triaxial test. Various image processing techniques were applied to the raw CT images to achieve a realistic three-dimensional (3D) reconstruction. Subsequently, particle point cloud data was processed through sampling, Gaussian noise injection, and grouping for training and testing the Poynton and PointNetLK networks. Next, the correspondences among particles across different scans were established by PointConv, and the transformation matrix between two mutually matched particles was predicted using PointNetLK. Finally, an examination of the changes in the spatial distribution and morphological parameters of both tracked and untracked particles throughout the shearing process was conducted and followed by an analysis of particle kinematics.

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

We 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 μ(I)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu (I)$$\\end{document} 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.