Mechanical 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.

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.

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.

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.

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.

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.

Granular behaviour under bi-directional shear with constant vertical stress and constant volume

This paper aims to investigate the role of bi-directional shear in the mechanical behaviour of granular materials and macro-micro relations by conducting experiments and discrete element method (DEM) modelling. The bi-directional shear consists of a static shear consolidation and subsequent shear under constant vertical stress and constant volume conditions. A side wall node loading method is used to exert bi-directional shear of various angles. The results show that bi-directional shear can significantly influence the mechanical behaviour of granular materials. However, the relationship between bi-directional shear and mechanical responses relies on loading conditions, i.e. constant vertical stress or constant volume conditions. The stress states induced by static shear consolidation are affected by loading angles, which are enlarged by subsequent shear, consistent with the relationship between bi-directional shear and principal stresses. It provides evidence for the dissipation of stresses accompanying static liquefaction of granular materials. The presence of bi-directional principal stress rotation (PSR) is demonstrated, which evidences why the bi-directional shear of loading angles with components in two directions results in faster dissipations of stresses with static liquefaction. Contant volume shearing leads to cross-anisotropic stress and fabric at micro-contacts, but constant vertical stress shearing leads to complete anisotropic stress and fabric at micro-contacts. It explains the differentiating relationship between stress-strain responses and fabric anisotropy under these two conditions. Micromechanical signatures such as the slip state of micro-contacts and coordination number are also examined, providing further insights into understanding granular behaviour under bi-directional shear.

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.

Cementor: A toolbox to generate bio-cemented soils with specific microstructures

Bio-cemented soils can exhibit various types of microstructure depending on the relative position of the carbonate crystals with respect to the host granular skeleton. Different microstructures can have different effects on the mechanical and hydraulic responses of the material, hence it is important to develop the capacity to model these microstructures. The discrete element method (DEM) is a powerful numerical method for studying the mechanical behaviour of granular materials considering grain-scale features. This paper presents a toolbox that can be used to generate 3D DEM samples of bio-cemented soils with specific microstructures. It provides the flexibility of modelling bio-cemented soils with precipitates in the form of contact cementing, grain bridging and coating, and combinations of these distribution patterns. The algorithm is described in detail in this paper, and the impact of the precipitated carbonates on the soil microstructure is evaluated. The results indicate that carbonates precipitated in different distribution patterns affect the soil microstructure differently, suggesting the importance of modelling the microstructure of bio-cemented soils.

An Improved Contact Force Model of Polyhedral Elements for the Discrete Element Method

The discrete element method (DEM) serves as a robust tool for simulating the mechanical behavior of granular materials. The accuracy of the DEM simulation is determined by the calculation of contact forces between elements. Compared to spherical elements, the contact modes of polyhedral elements are more complex. In this work, the contact force between polyhedral elements under different contact modes was investigated by experiment. Based on the experimental results, the normal stiffness coefficient in the Cundall’s contact model was modified. The improved contact force model was then applied in the DEM simulation and validated by means of comparison with the results of packing experiments. The research results demonstrate that the improved contact force model can be effectively applied to the simulation of different contact modes between polyhedral elements. The results of the packing experiment highly coincide with the results of the DEM simulation, which confirms the accuracy and reliability of the improved contact force model.

Poisson’s ratio of granular materials for Mohr-Coulomb elastoplastic model

ABSTRACT The Mohr-Coulomb elastoplastic model is extensively employed in geotechnical engineering. Despite the well-known nonlinear behaviour of granular cohesionless materials under a wide range of normal stress or confining pressure, the Mohr-Coulomb elastoplastic model continues to be largely used in geotechnical engineering, due to its simplicity and large availability in numerous commercialised software. Its application requires the input of a key parameter, named Poisson’s ratio. It is however a big challenge as its value changes with axial strain and confining pressure. In this study, the optimal Poisson’s ratio of granular materials for the Mohr-Coulomb elastoplastic model is determined by reproducing the experimental results of stress-strain relationships through numerical modelling with the Mohr-Coulomb elastoplastic model. The results show that the Poisson’s ratio μ 0.02, corresponding to the slope of the volumetric strain against axial strain curve at 2% of the peak deviatoric stress can be used in numerical modelling with the Mohr-Coulomb elastoplastic model as long as the granular material does not exhibit dilation behaviour. When the material exhibits dilation behaviour, the Poisson’s ratio μ 0.36, corresponding to the slope of the volumetric strain against axial strain curve at 36% of the peak deviatoric stress, seems to be appropriate in numerical modelling with the Mohr-Coulomb elastoplastic model. In addition, the study also shows that the Mohr-Coulomb elastoplastic model can be used to simulate mechanical behaviour of granular material under small strain, but not appropriate under large strain conditions.

Influence of the interparticle friction coefficient on the mechanical behaviour of breakable granular materials with realistic shape

Interparticle friction coefficient μ is an important factor affecting the mechanical properties of granular materials. In this study, the influence of μ on the mechanical behavior of granular materials is investigated by DEM. Through 3D scanning and Voronoi tessellations, the breakable particle model with realistic shape is constructed. A series of drained triaxial tests were performed at different μ values. Then, the particle breakage characteristics, including the degree of particle breakage and the breakage mode, were evaluated. In addition, microscopic characteristics, including coordination numbers and contact forces, were examined. Finally, the underlying mechanisms of φc evolution are explained from two perspectives of particle movement and fabric anisotropy. First, the rolling behavior of the particles increases with μ values, leading to a larger average displacement of particles. The influence of particle movement and friction coefficient balance each other, resulting in φc remaining constant when μ⩾0.4. Second, the initial increase of φc is due to the increase of the contact normal anisotropy ac, the normal contact force anisotropy an and the tangential contact force anisotropy at. Subsequently, the constant φc is the result of the decrease of ac and an being compensated by the increase of at.

Macro-micro Performances of Granular Materials Considering the Influences of Density and Stress Path under True Triaxial Conditions: A DEM Investigation

The mechanical behaviors of granular materials are dominated by internal structure, which are related to fabric evolution during loading. This study investigated the fabric evolution of granular materials with different densities and stress paths under true triaxial conditions. A series of discrete element numerical simulations with different intermediate principal stress coefficient b were carried out along the constant mean stress p and the constant minor principal stress σ3 stress paths for both loose and dense specimens. The results indicated that the constant-p stress path produced a faster increase in stress ratio than the constant-σ3 stress path at the same b. The effects of specimen density on the peak friction angle are greater than that of stress path. The microscopic analyses revealed that the constant-p stress path facilitates a much more preferential distribution of normal contact force network along the major principal direction. The discrepancies in the peak stress ratio under two stress paths were thus interpreted. The dense specimen will rapidly form a higher anisotropic distribution of the normal contact force network upon shearing, and its anisotropic intensity was almost twice that of the loose specimen at the peak stress state. In addition, a unique relationship between the strong deviatoric fabric ratio and stress ratio was presented. The ratio of the two was approximately 1.0 regardless of stress path, density and b value. Finally, an underlying relationship between the stress components and the whole fabric components at the critical state was confirmed by introducing a new stress tensor. The three principal components (F1, F2 and F3) of the whole fabric tensor can be quantitatively represented with the imposed three principal stress components (σ1, σ2 and σ3) by employing a relationship of F1:F2:F3 = σ10.27:σ20.27:σ30.27. It provides a more comprehensive perspective to analyze the macro-micro performances of granular materials at the critical state.

Finite element modeling of biomass hopper flow

Hoppers are widely used biomass handling devices that channel bulk biomass from storage to subsequent handling equipment. Jenike’s longstanding approach, based on the Mohr-Coulomb model, has been successfully used to design hoppers handling cohesionless granular materials such as grains and other agricultural produces. However, designing a hopper to ensure reliable biomass flow is found to be challenging due to cohesion, irregular particle shape, and bulk material elastoplasticity. This study aims to address the biomass handling engineering challenge with alternative constitutive material models concerning the flow behavior of bulk solids. Finite element modeling is an approach that allows for implementation of different material models, whose underlying constitutive theories assist in investigating the origin and manifestation of bulk mechanical behavior of granular materials. This study focuses on the incipient gravity hopper flow of two types of biomass feedstocks, i.e., ground corn stover and Douglas fir wood. Three widely used constitutive material models, i.e., Mohr-Coulomb model, modified Cam-Clay model, and Drucker-Prager/Cap model, are implemented. Using the flow pattern represented by the volume of biomass exhibiting more than 7% of axial strain (Kamath and Puri, 1999), the finite element model predicts that the bulk corn stover particulate material forms an arch, which represents a hampered transition from the static state to the dynamic flow-state out of the hopper, whereas bulk Douglas fir wood particulate material develops a reliable mass flow pattern. A laboratory scale hopper was used to experimentally determine the biomass flow conditions, which were subsequently compared with the predicted onset of flow by a finite element model (FEM). The developed FEM was found to correctly predict the initiation of mass flow for the milled Douglas fir wood, whereas corn stover was predicted to establish a strong core flow suggesting an unreliable handling characteristic. This observation aligns with the reported poor handling of milled corn stover.

Constitutive modelling of idealised granular materials using machine learning method

Predicting the constitutive response of granular soils is a fundamental goal in geomechanics. This paper presents a machine learning (ML) framework for the prediction of the stress-strain behaviour and shear-induced contact fabric evolution of an idealised granular material subject to triaxial shearing. The ML-based framework is comprised of a set of mini-triaxial tests which provide a benchmark for the setup and validation of the discrete element method (DEM) model of the granular materials, a parametric DEM simulation programme of virtual triaxial tests which provides datasets of micro- and macro-mechanical information, as well as a multi-layer perceptron (MLP) neural network which is trained and tested using the DEM-based datasets. The ML model only requires the initial void ratio of the granular sample as the input for predicting its constitutive response. The excellent agreement between the ML model prediction and experimental test and DEM simulation results indicates that the ML–based modelling approach is capable of capturing accurately the effects of initial void ratio on the constitutive behaviour of idealised granular materials, bypassing the need to incorporate the complex micromechanics underlying the macroscopic mechanical behaviour of granular materials. Lastly, a detailed comparison between the used MLP model and long short-term memory (LSTM) model was made from the perspective of technical algorithm, prediction accuracy, and computational efficiency.

Shape characteristics of granular materials through realistic particle avatars

The micro- and macroscale mechanical behaviors of granular materials strongly depend on the morphological features of the grains. Imaging techniques, such as X-ray computed tomography, have been used to scan realistic particle geometries and obtain shape characteristics. However, these methods are expensive, laborious, and only applicable to limited grain sizes. A simpler alternative would be to estimate 3D shape features from 2D digital photographs in the field, but they might be affected by image resolution and particle orientation. This study aims to assess the effect of image quality for shape characterization and obtain relationships between widely used 2D and 3D shape descriptors through randomly generated computational particle geometries termed ‘avatars.’ Additionally, X-ray μ-CT scans are performed on beach sand grains with irregular shapes. Particle avatar-based 2D-3D form relationships are compared with μ-CT data of 38 beach sand grains and at least 2300 particles of other material types from literature. Changes in the resolution of the images affected both geometrical and morphological features of the particles. Volume and surface area measurements are affected by the 3D image quality, and low-quality 2D digital images influenced shape characterization. From the observed relationships between 2D and 3D shape descriptors, some 3D shape characteristics such as true sphericity and convexity can be reliably approximated from 2D digital images of randomly oriented particles.

Evolution of the force chain structure of partially saturated granular material under triaxial compression conditions

Saturation conditions play a significant role in the mechanical behavior of granular material and the evolution of an interparticle contact system during the loading process. Using data derived from discrete element simulations of granular assemblies subject to triaxial compression loading with different suctions, we examine the properties of an interparticle contact network and force chain structure to provide a comprehensive picture of the evolution of a particle-scale contact system. The study focuses on the evolution of the topological statistic features (including degree and triangles) and the force chain structure characteristics influenced by suction conditions. To comprehensively evaluate the characteristics of the force chain system, combined statistical parameters are proposed for describing the linearization and intensity of the force chain structure, which account for multiple features of force chains. Accordingly, a novel expression combined with multiscale properties is proposed for strength prediction that convincingly explains data results in the studied suction range. This study illustrates the consistency of the evolving force chain structure features with mechanical behavior that provides new insights for understanding the particle-scale force chain structure evolution from which these properties dominate the macroscopic response.

DEM contact model for spherical and polyhedral particles based on energy conservation

The mechanical behaviors of granular materials are greatly influenced by the geometric shapes, which is widely investigated using the discrete element method (DEM). Accurate contact detection is a critical issue in modelling complicated contact types, especially for arbitrary shaped particles. In this study, the contact detection algorithms for spherical and polyhedral particles based on energy conservation are classified into polyhedron-polyhedron and sphere-polyhedron contacts. The polyhedron-polyhedron and sphere-polyhedron contact detection algorithms are developed under the DEM framework of Coupling Simulator (CoSim-DEM). Geometric dualization theory is used in the polyhedron-polyhedron contact detection algorithm to construct the overlapping volume of polyhedral particles. For the sphere-polyhedron contact detection, the algorithm can transfer into the contact between sphere and triangles composed of polyhedron, and the contact forces between arbitrary shaped particles can be calculated based on calculated contact characteristics. Particle collision tests with different particle shapes and contact types are used to validate the aforementioned algorithms. Experiments and simulation studies of deposition tests are conducted to validate the effectiveness and stability of algorithms. Furthermore, the rotating drum tests are used to analyze the influence of particle shapes on the calculation efficiency. Finally, a large-scale rotating drum test involving different kinds of particles with random sizes is performed, demonstrating the robustness of algorithms based on CoSim-DEM.

Experimental investigation of the shape effect on the mechanical behavior of granular materials under uniaxial loading with lateral confinement

Experimental investigation of the shape effect on the mechanical behavior of granular materials under uniaxial loading with lateral confinement