Response Of Granular Materials Research Articles

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.

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.

Macro-micro mechanical study of principal stress rotation in granular materials using DEM simulations of hollow cylinder test

The dependency of sand behavior anisotropy on microstructure reveals the importance of macro-micro mechanical analysis of the principal stresses rotation effect on the strength-deformation response of granular material. In this study multi-scale analysis of the granular material's behavior using three-dimensional discrete element method simulations of the hollow cylinder test was presented. The effect of principal stresses rotation (α) on the macro-mechanical behavior of the soil was investigated from the micro-mechanical anisotropy aspect. It was observed that principal stress rotation affects the anisotropy coefficient and directional distribution of all micro-parameters which can change the soil's behavior according to loading conditions. The stress-force-fabric relationship was used to analyze the microstructure's stress state based on micro-parameters anisotropy coefficients. In addition to the good agreement between stress-force-fabric and general stress tensors, the decreasing trend of the maximum deviator stress and internal friction coefficient angle with increasing α can be observed for both stress tensors.

Quantifying fabric anisotropy of granular materials using wave velocity anisotropy: a numerical investigation

Fabric anisotropy is a sought-after micro index to correlate macro mechanical responses of granular materials. In this work, the discrete-element method is utilised to simulate multi-directional bender element tests in granular soils to obtain the evolution of wave velocities during drained conventional triaxial (CT) and true triaxial (TT) tests; the contact normal-based fabric is simultaneously monitored for bridging the fabric anisotropy and wave velocity anisotropy. The results show that stress-normalised wave velocities and microscopic fabric, including contact normal distribution and coordination number, remain nearly constant until a stress ratio threshold is reached. After the threshold value is reached, stress-normalised wave velocities start to decrease, especially in the minor principal stress direction, accompanied by significant adjustment of coordination number and fabric anisotropy. The results also reveal that the normalised wave velocity depends on the contact normal densities in the wave propagation and particle oscillation directions. With the contact normal distribution represented by a density function, a good linear relationship between the microscopic fabric anisotropy and macroscopic wave velocity anisotropy is obtained for both CT and TT tests.

Linking the macro-scale response of granular materials during drained cyclic loading to the evolution of micro-structure, contact network and energy components

This study has considered the behaviour of granular materials subjected to drained cyclic loading under constant mean effective stress. Using the discrete element method, cubical, isotropically compressed samples were subjected to 50 loading cycles at different values of mean stress (p' = 100, 200, 300 kPa) and different loading amplitudes (zeta = 5%, 10% and 20% of p'). At low cycle numbers, the deformation mechanism is controlled by contractive volumetric strains, before transitioning to the ratcheting regime, characterised by the persistent accumulation of plastic strains. An energy/work analysis showed that the volumetric work per cycle decreased as hysteresis loops tighten. During ratcheting, most boundary work was dissipated by contact sliding. The mechanical response was controlled by zeta, with little to no influence of p'. For zeta = 5%, deformations were confined to the elastic range, with no increase in secant stiffness G_{sec} or shear strength after cyclic loading. For zeta = 10%, G_{sec} and the shear strength increased after cyclic loading, although no significant expansion of the yield surfaces was observed. The largest loading amplitude (zeta = 20%) induced yielding at low cycles, leading to significant changes in the fabric, volume and yield surfaces of the samples, and a significant increase of shear strength and G_{sec}. At the micro-scale, graph theory was used to quantify the evolution of the contact network. After sim 20 loading cycles, the network reached a steady-state of constant but persistent topology changes in the material, with most of the topology retained between loading cycles.

Spatial clustering of microscopic dynamics governs the slip avalanche of sheared granular materials

Establishing quantifiable links between individual-particle dynamics and macroscopic response of granular materials has been a longstanding challenge, with implications in material science, geology and industry. Despite sustained efforts in uncovering generic features in both macroscopic flow and microscopic dynamics, further advance on the subject matter demands quantitative correlations to be established. We propose a 3D convolution neural network (CNN) to quantify the link between microscopic dynamics and macroscopic stress fluctuations, including both stress recharge (stick regime) and stress drop (slip regime). Through the model interpretation, microscopic dynamics is found to demonstrate distinctive spatial patterns in the stick and slip regimes, which root in the result of free volume-induced structural rearrangements and contact network dynamics, respectively. We conclude that the spatial clustering of microscopic dynamics governs the occurrence of slip avalanches and acts as the “fingerprint” of macroscopic stress fluctuation. The data-driven framework developed in this paper can be readily extended to other amorphous solids for building cross-scale relations, paving a new way to understand the complex behavior of amorphous solids.

Experimental study on horizontal pressure of column-supported concrete group silos under earthquake force

ABSTRACT The overpressure of silo wall caused by granular materials under earthquake is one of the main reasons of silo damage. Two shaking table model tests were carried out with column supported silos and independent single silos, respectively. The seismic response of silo granular materials was analyzed first, and then the dynamic lateral pressure of silo wall under different levels of earthquake and overpressure coefficient were obtained. The results showed that the interaction between the granular materials and the silo wall in the group silos is related to the position of the individual silo. The seismic response of granular materials is linked with the spectral characteristics of seismic waves. The overpressure coefficients of the corner silo and the side silo are greater than that of the independent single silo with a 7% and 9% higher value, respectively. Apparently, the seismic response characteristics of the independent single silo are totally different from that of the group silos. It was concluded that when designing the wall of the group bin, the position of the bin should also be considered.

Relationship between acoustic emission and energy dissipation: a DEM study of soil–structure interaction

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 paucity of understanding of the fundamental links between particle-scale mechanisms and AE generation in particulate materials, which limits interpretation of the measured AE. The objective of this study was to establish links between particulate-scale energies and AE activity measured at the macro-scale in experiments. To achieve this, a programme of 3D DEM simulations was performed on granular soil/steel structure interfaces and the results were compared with experimental measurements. The findings show that the fundamental particulate-scale mechanisms that contribute to AE generation are friction and damping in particulate rearrangement, with friction being the dominant mechanism (i.e. > 95% of the total energy). Dissipated plastic energy was influenced in the same way as measured AE activity by unload–reload behaviour, imposed stress level, mobilised shearing resistance, and shearing velocity. Relationships have been established between AE and dissipated plastic energy (R2 from 0.96 to 0.99), which show AE generated per Joule of dissipated plastic energy is significantly greater in shearing than compression. A general expression has been proposed that links AE and plastic energy dissipation. This new knowledge enables improved interpretation of AE measurements and underpins the development of theoretical and numerical approaches to model and predict AE behaviour in particulate materials.

Contact Overlap Calculation Algorithms and Benchmarks Based on Blocky Discrete-Element Method

The mechanical response of granular materials has been investigated widely using discontinuous modeling, such as the discrete-element method (DEM). Contact detection and contact resolution have been critical issues when modeling multiple body contacts, especially for arbitrary polyhedral blocks. In this study, the contact overlap calculation algorithms, including polyhedron–polyhedron and polyhedron–boundary contact, were developed to calculate the contact characteristics. For polyhedron–polyhedron contact, the contact overlap volume algorithm is developed based on the geometric dualization theory. The Gilbert–Johnson–Keerthi (GJK) and Quickhull algorithms are used to calculate the overlap polyhedron. The contact characteristics, such as normal direction (n), contact area (a), and penetration depth (un) could be extracted from the contact overlap volume. For polyhedron–boundary contact, a novel and effective algorithm is presented, where the polyhedron–boundary contact is transformed into polyhedron–triangle contact. Then, two types of benchmarks are used to verify the previously mentioned algorithms, which demonstrated that the algorithms could handle the complicated contact types and maintained contact continuity even from face to edge contact. As a complex benchmark, the failure process in a masonry structure is simulated and compared with the model test.

Data-driven strain–stress modelling of granular materials via temporal convolution neural network

Machine learning offers a new approach to predicting the path-dependent stress–strain response of granular materials. Recent studies show that temporal convolution neural (TCN) networks, a mutation of the 1D convolution neural network (CNN), have a powerful capability of addressing time-related prediction tasks. In this work, TCN networks are constructed to explore their potential in capturing the constitutive law of granular materials. To train and test the TCN network, three types of numerical experiments are implemented to generate datasets via discrete element modelling. The Bayesian optimisation method is employed to find the optimum architecture of the network. Furthermore, to improve the training accuracy and efficiency, a transfer learning (TL) scheme is innovatively leveraged, which utilises the trained network parameters from a set of shorter time steps and/or coarser data points of the training strain–stress loading curves, as the initial values, to train the network for a longer time step. The prediction ability of the trained TCN network is assessed and compared with a recurrent neural network which has been proved to perform well in predicting constitutive laws of the granular materials. In addition, training datasets with artificially added noise are also used to test and analyse the robustness of TCN networks.

Linking inherent anisotropy with liquefaction phenomena of granular materials by means of DEM analysis

The liquefaction phenomena of sands have been studied by many researchers to date. Laboratory element tests have revealed key factors that govern liquefaction phenomena, such as relative density, particle size distribution, and grain shape. However, challenges remain in quantifying inherent anisotropy and in evaluating its impact on liquefaction phenomena. This contribution explores the effect of inherent anisotropy on the mechanical response of granular materials using the discrete element method. Samples composed of spherical particles are prepared which have approximately the same void ratio and mean coordination number (CN), but varying degrees of inherent anisotropy in terms of contact normals. Their mechanical responses are compared under drained and undrained triaxial monotonic loading as well as under undrained cyclic loading. The simulation results reveal that cyclic instability followed by liquefaction can be observed for loose samples having a large degree of inherent anisotropy. Since a sample having initial anisotropy tends to deform more in its weaker direction, leading to lower liquefaction resistance, a sample having an isotropic fabric potentially exhibits the greatest liquefaction resistance. Moreover, the effective stress path during undrained cyclic loading is found to follow the instability and failure lines observed for static liquefaction under undrained monotonic loading. From a micromechanical perspective, the recovery of effective stress during liquefaction can be observed when a threshold CN develops along with the evolving induced anisotropy. Realising that the conventional index of the anisotropic degree (a) is not effective when the CN drops to almost zero during cyclic liquefaction, this contribution proposes an alternative index, effective anisotropy (a×CN), with which the evolution of induced anisotropy can be tracked effectively, and common upper and lower bounds can be defined for both undrained monotonic and cyclic loading tests.