Mechanical Behavior Of Granular Materials Research Articles

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.

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.

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.

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.

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

A breakage matrix methodology to predict particle size evolution of calcareous sands

Breakage-induced evolution of particle size distribution (PSD) will greatly affect the mechanical behavior of granular materials, and has been an important concern in geotechnical engineering. This paper presents a breakage matrix approach to investigate the evolution of PSD with detailed breakage information of each single-sized particles via conducting one-dimensional compression tests on dyed calcareous sands with different initial conditions. The breakage of each single-sized particles of soil samples with multi-sized particles under different initial conditions was analysed by the PCAS image recognition technologies. It has been found that the breakage-induced PSD of each single-sized particles of the soil samples tends to be fractally distributed, regardless of their initial PSDs. Furthermore, the degree of particle breakage of each single-sized particles is linearly related with the input work per unit volume. Finally, the proposed model establishes the breakage matrices of both uniform and gap-graded calcareous sands, which demonstrates its satisfactory performance.

Analysis of the effect of unbound granular base characteristics on the performance of flexible pavements

The influence of aggregate properties on the mechanical behaviour of granular materials is widely recognized in the literature, but default values are considered most of the time for pavement design. This limits their consideration to accepting materials that show values in defined ranges of indicative properties. It is expected that materials with similar particle size distributions but different characteristics will perform differently. This work evaluated the influence of considering the characteristics of the aggregate base and its effect on stiffness and damage. Two approaches were used to modify the adjustment coefficients in stress-dependent resilient modulus models to consider the characteristics of the granular materials. The results showed that thin pavements were particularly sensitive to these characteristics, with pavement capacity expected to be higher than in default models when considering crushed aggregates. In contrast, the capacity may be as low as 40% of the conventional estimate for partially crushed aggregates.

A predictive deep learning framework for path-dependent mechanical behavior of granular materials

A predictive deep learning framework for path-dependent mechanical behavior of granular materials

Influence of small particle surface asperities on macro and micro mechanical behavior of granular material

AbstractThe shape of particles can have a great impact on the mechanical behavior of granular material, which is not only limited to general shape measures such as sphericity and roundness, but also applies for small scale measures such as surface asperities. In this study, triaxial tests on 3D printed particles and DEM tests show that small surface asperities on spherical particles can contribute significantly to the peak strength and dilatancy of granular material, which cannot be reflected by simply altering the traditional contact parameters in DEM. Using polydispersed particles with artificially designed surface asperities in the form of bumps for laboratory and DEM triaxial tests, both macro and micro scale behavior of granular material are analyzed to reveal the influence of these small surface asperities. The result shows that surface asperities can change the coordination number, anisotropy, and normal contact force on the micro scale, increasing the interlocking between particles and restricting particle rotation, which leads to the increase of peak strength and dilatancy on the macro scale. Although the commonly adopted approach of introducing rolling resistance to reflect shape influence can help to enhance the simulation of stress‐strain relationship, especially for particles with relatively small artificial asperities, the micro scale influence of rolling resistance and surface asperities are found to be different as the size of the asperities increase.

Uticaj trostruke veličine čestica na mehaničko ponašanje zrnastih materijala primeno metode diskretnih elemenata (MDE)

Granules are used in various industries such as medicine and agriculture, and their behavior is influenced by the characteristics of the constituent particles. The Discrete Element Method (DEM) is a technique for characterizing the mechanical behavior of granular materials by building a mechanical model that describes the impacted parameters, including particle shape, which is being one of these parameters. As a result, the discrete element method is applied to investigate the macro-and micro-mechanical shear behavior of granular materials. For this study, a gravitational disposition for geometrical arrangement model has been used to model various triple particle sizes for a direct shear test using (EDEM®), which is a three-dimensional (3D) program based on (DEM). Different triple particle sizes were used to create an assembly. The results revealed that the size index affected the relationship between shear strength, angular velocity, dilation, coordination number (CN), and volumetric strain.

Use of machine learning for unraveling hidden correlations between particle size distributions and the mechanical behavior of granular materials

A data-driven framework was used to predict the macroscopic mechanical behavior of dense packings of polydisperse granular materials. The discrete element method, DEM, was used to generate 92,378 sphere packings that covered many different kinds of particle size distributions, PSD, lying within 2 particle sizes. These packings were subjected to triaxial compression and the corresponding stress–strain curves were fitted to Duncan–Chang hyperbolic models. An artificial neural network (NN) scheme was able to anticipate the value of the model parameters for all these PSDs, with an accuracy similar to the precision of the experiment and even when the NN was trained with a few hundred DEM simulations. The estimations were indeed more accurate than those given by multiple linear regressions (MLR) between the model parameters and common geotechnical and statistical descriptors derived from the PSD. This was achieved in spite of the presence of noise in the training data. Although the results of this massive simulation are limited to specific systems, ways of packing and testing conditions, the NN revealed the existence of hidden correlations between PSD of the macroscopic mechanical behavior.

Prediction of 3D contact force chains using artificial neural networks

Contact force chains (CFCs) in the heterogeneous granular materials are often considered to be structured physical systems that play a key role in their mechanical properties such as stiffness, strength, stability and flowability. In this context, quantitatively estimating the evolution of CFCs in a quasi-statically sheared granular system is essential for advancing our understanding of the mechanics of granular materials. In this paper, based on discrete element method (DEM) simulation data, an artificial neural network (ANN) is developed and applied to predict the anisotropy of the CFCs in two types of idealized granular materials with different initial relative densities undergoing triaxial shearing. Five features including particle size, coordination number and particle displacement (i.e., x-, y- and z-components of the particle displacement) at the particle-scale and the meso-scale each are used to train and test the established ANN model. The results of model prediction show that the 3D orientational distributions of the CFCs from the ANN predictions match very well the DEM simulation results during the whole shearing progress. It is found that for both dense and loose samples, the combined set of particle-scale and meso-scale features have a dominating influence on the CFC evolutions but the ANN model performs better in the CFCs estimation at the strain increment of 0–7% than at the strain increment of 7%–14%. The outcome of this study shows that machine learning is a promising tool for studying the complex mechanical behavior of granular materials.