Response Of Granular Materials Research Articles

Effect of Rate-Dependent Breakage on Strength and Deformation of Granular Sample—A DEM Study

The mechanical response of granular materials is influenced significantly by both the magnitude and strain rate. While traditionally considered rate-independent in the quasi-static regime, granular media can exhibit rate effects in certain instances. This research uses two-dimensional discrete element modelling (DEM) to investigate the rate effects in one-dimensional compression tests by comparing non-crushable with crushable granular samples. This study indicates that micromechanical properties such as particle breakage and contact force distributions are predominant factors in dictating the macroscopic responses of the material. The DEM simulations highlight differences in macroscopic changes between crushable and non-crushable samples, demonstrating a clear correlation between mechanical properties and underlying microstructural features. Notably, the distribution of contact forces varies with strain rates, influencing the degree of particle breakage and, consequently, the overall rate-dependent behaviour. Further, this study explores the impact of post-breakage contact creation and progressive force redistribution, which contributes to observable differences in macroscopic stress under varying loading rates, which is quantified using coordination number, particle velocity, and fabric tensor profiles at two loading rates.

Mesoscale simulation of granular materials under weak shock compaction–pore size distribution effects

This research established a systematic method to generate various pore-size distributions (PSDs) and studied the effect of PSDs on the shock compaction response of granular materials using two-dimensional mesoscale simulations under identical porosity. Simulations utilized various PSDs for three particle shapes (circle, ellipse, and square). Contacting particle configurations using three PSDs, characterized by spatially uniform distributed pores to heterogeneous distributed pores, and non-contacting particle configurations under a single case of PSD were tested. The PSD of generated particle sets was characterized using coordination number, mean diameter, and bimodality coefficient as statistical metrics. Mesoscale simulations showed that regardless of the conditions of pore distributions, shock compaction of granular materials consistently demonstrates a precursor, shock compaction front, and end. However, the shock compaction velocity of contacting particles was dependent on the PSDs despite the constant initial porosity. The compaction velocity was faster in particle configurations with relatively uniform pore distributions than in heterogeneous pore distributions, which our study demonstrated can be attributed to particle rearrangement during compaction. Circular-shaped particles had high sensitivity in shock compaction response to the various PSDs. Furthermore, a contacting particle configuration tended to propagate the shock compaction wave relatively faster than particles that were in a non-contact configuration. This study established the relative importance of considering PSD as a metric over the coordination number in studies of the shock compaction response of granular materials. Further, insights are provided on the evolving shock substructure to characterize the shock compaction response of granular materials.

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.

Modeling the impact of terrain surface deformation on drag force using discrete element method and empirical formulation

Understanding motion-induced terrain deformation is essential for improving predictive models in geotechnical engineering, infrastructure development, and robotics. The existing analysis assumes a uniform and unchanged environment and lacks a description of the terrain deformation induced by motion, which is particularly significant when the grains are loosely packed. To address this gap, we performed numerical investigations to mathematically model the changes in the surrounding environment and their corresponding effects on resistance. Specifically, we examined the response of granular materials and the energy variation of the particles during motion. Increased energy in the direction of motion was categorized as influences above or below the medium surface. Aligned with the influencing factors, two variables were considered to quantify the impact on the drag force. Building upon the energy analysis and the framework of Resistive Force Theory, we proposed a drag force model for buried motion in loose granular terrain. Compared with the experimental data, the average predictive error decreased from 17.8% to less than 2.7%. Our study provides a feasible approach for incorporating the effects of terrain deformation into a drag force model, thereby enhancing the accuracy and contributing to the development of granular locomotion.

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.

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.

Rolling table centrifuge modelling of partially saturated granular material to inform on instability during solid bulk cargo transport

The response of partially saturated granular cargoes during maritime transportation has resulted in the capsize and sinking of 27 bulk carriers at sea and the loss over 90 seafarers’ lives in the last decade. The partially saturated granular material response to energy imparted during cargo loading, ship engine vibrations and vessel rolling motions from sea states causes a change in state of the granular cargo, which can lead to vessel instability and ultimately capsize. However, the mechanisms driving the response of partially saturated granular cargos within a bulk carrier hold are not well understood. This paper presents results from an experimental study of rolling table centrifuge model tests on a partially saturated silica sand to contribute to improved understanding of the response of granular cargoes during maritime transport. Observed settlement, pore pressure, moisture content and density changes during and/or following a sequence of large amplitude rolling motions are presented. The results indicate that for the conditions considered, a progressive upwards migration of pore water during rolling led to creation of a free surface of water above the granular sample that was left in a denser, lower moisture content sample compared to its initial state. Sloshing of free water on top of even a competent cargo during rolling motions of the ship can contribute to loss of ship stability and ultimately capsize.

Emergence of critical state in granular materials using a variationally‐based damage‐elasto‐plastic micromechanical continuum model

AbstractThe mechanical response of granular materials, exemplified by frictional grain interactions, is characterized by a critical state in which deformation occurs without change of material volume or stresses when subjected to large shear deformation. In this work, a granular micromechanics approach (GMA) based continuum model is used to investigate the emergence of such a critical state. The continuum description is constructed through mechanical concepts based upon elastic and dissipation energies defined for a generic grain‐pair interaction. A hemivariational principle provides the basis for considering the evolution of damage and plasticity phenomena comprising grain‐pair contact loss and irreversible deformation. As a consequence, the Karush–Kuhn–Tucker (KKT)‐type conditions are derived, which give the evolution equations for the irreversible phenomena. Notably, in this derivation there is no invocation of flow rules and other similar assumptions of classical phenomenological continuum damage and plasticity. Further, Piola's ansatz is elaborated to kinematically connect granular micromechanics of grain‐pair to the continuum description. While the concept of critical state analysis has been handled with either phenomenological approaches or discrete numerical frameworks, in the present paper this concept is examined within a micromechanics‐based continuum description. The constitutive model is established and the coupled damage and plastic irreversible quantities are assessed. The critical state is shown to emerge as grain‐pair related damage and plastic evolution in a competitive/collaborative manner during the imposed loading path.

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.

Thermal shakedown in granular materials with irregular particle shapes

Granular materials with irregular particle shapes undergo a myriad of temperature variations in natural and engineered systems. However, the impacts of cyclic temperature variations on the mechanics of granular materials remain poorly understood. Specifically, little is known about the response of granular materials to cyclic temperature variations as a function of the following central variables: particle shape, applied stress level, relative density, and temperature amplitude. This paper presents advanced laboratory experiments to explore the impacts of cyclic temperature variations on the mechanics of granular materials, with a focus on sands. The results show that cyclic temperature variations applied to sands induce thermal shakedown: the accumulation of irreversible bulk deformations due to microstructural rearrangements caused by thermal expansions and contractions of the constituting particles. The deformation of sands caused by thermal shakedown strongly depends on particle shape, stress level, relative density, and temperature amplitude. This deformation is limited for individual thermal cycles but accumulates and becomes significant for multiple thermal cycles, leading to substantial compaction in sands and other granular materials, which can affect various natural and engineered systems.

A two-scale study on the influence of biopolymer enhancement on drying granular materials

Cracking resulting from drying (constrained dehydration) poses a significant challenge in geomaterials, impacting their mechanical performance. To address this problem, extensive efforts have been made to prevent or mitigate the occurrence of cracks, with recent attention focused on the utilisation of biopolymers. This letter investigates the influence of varying concentrations of the xanthan biopolymer on the mechanical response of granular materials, examining both macro and micro scales. The strength changes of the soil were evaluated through desiccation experiments, analysing the appearance and progression of failure on the macro scale. The findings of this study demonstrate that failure (cracking) progression is mitigated and eventually eliminated by increasing the concentration of the additive xanthan. Additionally, capillary experiments were conducted to assess the changes in attraction and the development of capillary bridges on the micro-scale. They indicate that the formation of hydrogel bridges significantly enhances particle attraction, thereby increasing its macro-resistance to cracking.

On rapid compaction of granular materials: Combining experiments with in-situ imaging and mesoscale modeling

Grain and pore kinematics are important features of the response of granular materials to impact loading and rapid compaction. These kinematics and the associated material-phase stresses control solidification processes in shock-driven manufacturing and ignition in energetic materials. Diagnostics used in traditional gas-gun experiments cannot resolve spatially-heterogeneous grain and pore kinematics during granular compaction. Similarly, continuum models of the granular compaction process do not account for this spatial heterogeneity, making predictions of solidification or ignition challenging. Here, we propose a method of accessing spatially-heterogeneous grain and pore behaviors during rapid compaction which involves x-ray tomography, in-situ x-ray phase contrast imaging, and mesoscale numerical modeling. We use this method to study heterogeneous grain and pore kinematics and local stresses in a ductile aluminum powder impacted at velocities up to 800 m/s. We first validate the mesoscale model by comparing its predictions with x-ray measurements from an impact experiment on a sample that was used to generate a numerical microstructure. We then quantify the evolution of variables such as 3D pore sizes and local stresses. We comment on the role of microstructure on the granular material’s response and the sensitivity of the material response to changes in structure, impact velocity, and sample size.

Strain localization in the standard triaxial tests of granular materials: Insights into meso‐ and macro‐scale behaviours

AbstractThe standard triaxial tests cease to be valid as material tests since the homogeneity of the granular mass is lost when localized failures such as shear bands occur requiring a different approach to interpreting and analyzing material responses at the meso scale from the macro behaviour. This study sheds light on the above issue by analyzing the standard triaxial tests of the granular specimens undergoing localized failure at different scales using DEM. For the first time, the behaviour of material inside and outside of the shear band as well as the entire sample are quantitatively quantified through DEM simulations. The results enable confirmation of various theoretical hypotheses and experimental observations on the localized failure in granular materials. For example, by quantifying the inter‐particle contact forces of materials inside and outside the shear band zone, it is confirmed that the material outside the localization band undergoes inelastic unloading beyond the bifurcation point, while those inside the localization band experience inelastic shearing to reach the critical state. Moreover, the analysis in this study suggests that if the volume of the localization zone can be precisely measured from the experiment, the mesoscale constitutive responses that truly represent the inelastic behaviour can be quantified. This gives rise to a more appropriate method to obtain inelastic constitutive responses of granular materials from specimens undergoing localized failure in triaxial tests.

Sensitivity of G0 and stress-strain relation of geomaterials to grain shape and surface roughness

It is empirically known that the packing property and mechanical responses of cohesionless granular materials are influenced by grain shape. For example, the attainable range of void ratio depends on grain shape; angular materials tend to exhibit greater friction angles. Besides, shear wave velocity (Vs ) and small-strain shear modulus (G0 ) of sphere assemblies are affected by surface roughness. However, consensus has yet to be reached on the combined effect of grain shape and surface roughness on G0 and stress-strain relation. This contribution aims to evaluate the shape-roughness combined effect on the strain-dependent mechanical responses of granular materials. Three groups of glass beads having different grain shapes and a silica sand were used, and their grain surfaces were roughened through a systematic procedure using a milling machine. In total, eight materials were subjected to triaxial compression after measurement of Vs. The experimental results reveal that the stress-strain relation of angular particles is remarkably affected by the surface roughness, whereas the roughness effect on the stress-dependent variation in G0 is limited for angular particles.

A refined deviatoric hardening plastic model for sand

The classical deviatoric hardening models are capable of characterizing the mechanical response of granular materials for a broad range of degrees of compaction. This work finds that it has limitations in accurately predicting the volumetric deformation characteristics under a wide range of confining/consolidation pressures. The issue stems from the pressure independent hardening law in the classical deviatoric hardening model. To overcome this problem, we propose a refined deviatoric hardening model in which a pressure-dependent hardening law is developed based on experimental observations. Comparisons between numerical results and laboratory triaxial tests indicate that the improved model succeeds in capturing the volumetric deformation behavior under various confining/consolidation pressure conditions for both dense and loose sands. Furthermore, to examine the importance of the improved deviatoric hardening model, it is combined with the bounding surface plasticity theory to investigate the mechanical response of loose sand under complex cyclic loadings and different initial consolidation pressures. It is proved that the proposed pressure-dependent deviatoric hardening law is capable of predicting the volumetric deformation characteristics to a satisfactory degree and plays an important role in the simulation of complex deformations for granular geomaterials.

Static and cyclic liquefaction of granular materials considering grain morphology

In this study, a series of undrained monotonic and cyclic triaxial shear tests were performed on glass sands to evaluate the effect of grain morphology on the static and cyclic undrained response of granular materials. The grain morphology of five test materials prepared with two glass sands with significant shape discrepancy was quantified with an image-based method. The test results show that as the overall regularity decreases, the peak and steady state stress ratios increase, and the dilatancy is suppressed. The development of excess pore water pressure and accumulated axial strain as well as the rate of stiffness degradation are lowered as the overall regularity decreases. The results also reveal that excess pore water pressure is correlated well with the cyclic stiffness degradation index. The liquefaction resistance decreases with the increase of the overall regularity.

Acoustic emission and energy dissipation in soils during triaxial shearing

Acoustic emission (AE) monitoring offers the potential to sense particle-scale interactions that lead to macro-scale responses of granular materials. However, there remains a gap in fundamental understanding of how particle-scale mechanisms and properties influence AE generation, which limits the application of AE monitoring and interpretation of AE measurements. Addressing this gap in knowledge was the principal focus of this study. A benchmarking study was conducted first whereby a programme of seven 3D DEM simulations of drained triaxial tests with energy tracking were performed and compared with experimental measurements, which ensured the adopted simulation approach captured realistic behaviour. Dissipated plastic energy was influenced in the same way as measured AE by imposed confining pressure, displacement rate, and load-unload-reload compression and shearing. A parametric analysis was subsequently conducted using a programme of 25 3D DEM simulations. The findings show that sliding and rolling friction were the dominant mechanisms in plastic energy dissipation and hence particle-scale properties that influence sliding and rolling friction have the most significant influence on AE generation (e.g., particle shape, surface roughness, hardness). Relationships have been established to quantify how changes in particle-scale properties in DEM (sliding and rolling friction coefficients, normal and shear stiffness and their ratio, and local damping coefficient) lead to changes in dissipated plastic energy (R2 of 0.99); however, it should be noted that the relations in the sensitivity analysis cannot be interpreted as representative of specific granular materials. This new knowledge enables improved interpretation of AE and underpins the development of theoretical and numerical approaches to model and predict AE behaviour in particulate materials.

Systematic effect of particle roundness/angularity on macro- and microscopic behavior of granular materials

Roundness/angularity is a vital shape descriptor that significantly impacts the mechanical response of granular materials and is closely associated with many geotechnical problems, such as liquefaction, slope stability, and bearing capacity. In this study, a series of biaxial shearing tests are conducted on dual-size aluminum circular and hexagonal rod material. A novel image analysis technique is used to estimate particle kinematics. A discrete element model (DEM) of the biaxial shearing test is then developed and validated by comparing it with the complete experimental data set. To systematically investigate the effect of roundness/angularity on granular behavior, the DEM model is then used to simulate eight non-elongated convex polygonal-shaped particles. Macroscopically, it is observed that angular assemblies exhibit higher shear strengths and volumetric deformations, i.e., dilations. Moreover, a unique relationship is observed between the critical state stress ratio and particle roundness. Microscopically, the roundness shows a considerable effect on rotational behavior such that the absolute mean cumulative rotation at the same strain level increases with roundness. A decrease in roundness results in relatively stronger interlocking, restricting an individual particle’s free rotation. Furthermore, the particles inside the shear band exhibit significantly higher rotations and are always associated with low coordination numbers. Generally, the geometrical shape of a particle is found to have a dominant effect on rotational behavior than coordination number.Graphical

Fingering and strain localization in porous media during imbibition processes

SummaryFingered infiltration of a wetting fluid through a porous network is a widely studied subject in the field of fluid mechanics. However, the effect of this heterogeneous percolation on the response of granular materials, in particular fine‐grained soils, is a poorly investigated and badly understood topic which deserves deep analysis, considering, among others, possible applications in soil remediation and underground energy storage. This paper presents a first application of a new formulation of unsaturated poromechanics based on a phase field approach that allows to characterize on the one hand the occurrence of fingering hydraulic instabilities and on the other one to capture their effects on the irreversible, and possible unstable, deformation of the solid skeleton. The envisaged application concerns the behavior of fine‐grained soils whose dilatant/contractant behavior is more and more attracting the interest of the scientific community both in the fields of experimental research and numerical modeling.