A DEM study on microstructural behaviour of soluble granular materials subjected to chemo-mechanical loading

The behavior of granular materials mainly depends on the mechanical and engineering properties of particles in its structural matrix. Crushing or breakage of granular materials under compression or shear occurs when the energy available is sufficient to overcome the resistance of the material. Relatively little systematic research has been conducted regarding how to evaluate or quantify particle crushing and how it effects the engineering properties of the granular materials. The aim of this study is to investigate the effect of crushing on the bulk behavior of granular materials by using manufactured granular materials (MGM) rather than using a naturally occurring cohesionless granular material. MGM allow changing only one particle parameter, namely the “crushing strength”. Four different categories of MGM (with different crushing strength) are used to study the effect on the bulk shear strength, stiffness modulus, friction and dilatancy angle “engineering properties”. A substantial influence on the stress–strain behavior and engineering properties of granular materials is observed. Higher confining stress causes some non-uniformity (strong variations/jumps) in volumetric strain and a constant volumetric strain is not always observed under large shear deformations due to crushing, i.e. there is no critical state with flow regime (with constant volumetric strain).

Previous research studies have used either physical experiments or discrete element method (DEM) simulations to explore, independently, the influence of the coefficient of inter-particle friction (μ) and the intermediate stress ratio (b) on the behaviour of granular materials. DEM simulations and experiments using photoelasticity have shown that when an anisotropic stress condition is applied to a granular material, strong force chains or columns of contacting particles transmitting relatively large forces, form parallel to the major principal stress orientation. The combined effects of friction and the intermediate stress ratio upon the resistance of these strong force chains to collapse (buckling failure) are considered here using data from an extensive set of DEM simulations including triaxial and true triaxial compression tests. For all tests both μ and b affected the macro- and micro-scale response, however the mechanisms whereby the force chain stability was improved differ. While friction clearly enhances the inherent stability of the strong force chains, the intermediate stress ratio affects the contact density and distribution of orthogonal contacts that provide lateral support to the force chains.

A topological view on microscopic structural evolution for granular material under loading and unloading path

The paper describes a series of tests performed in a drum centrifuge on instrumented model displacement piles in normally consolidated sand. These tests examined the influence of the pile installation method, the stress level, and the pile aspect ratio on the increase in lateral effective stress on the pile shaft during static load testing to failure. A parallel series of constant normal load and constant normal stiffness (CNS) laboratory interface shear experiments was performed to assist interpretation of the centrifuge tests. It is shown that although the cycling associated with pile installation results in a progressive reduction in the stationary horizontal effective stress acting on a pile shaft and densification of the sand in a shear band close to the pile shaft, this sand dilates strongly during subsequent shearing to failure in a static load test. The dilation (the amount of which depends on the cyclic history) is constrained by the surrounding soil and therefore leads to large increases in lateral effective stresses and hence to large increases in mobilized shaft friction. The increase in lateral stress is shown to be related to the radial stiffness of the soil mass constraining dilation of the shear band and to be consistent with measurements made in appropriate CNS interface shear tests. The paper's findings assist in the extrapolation of model-scale pile test results to full-scale conditions.Key words: sand, displacement pile, centrifuge tests, shaft friction.

The objective of this paper is to resolve different length scales in structure analysis using an interface coupling the discrete element method (DEM) with the finite element method (FEM). This approach distinguishes itself from other methods in so far that no overlapping domains between finite and discrete elements exist. Both domains are separated in the physical space and the numerical simulation domain. The proposed approach is relevant to almost all engineering applications that deal with granular matter such as storage in hoppers, transport on conveyor belts or the displacement of granular material as in mixers or the excavation of the soil. For these applications an engineering device such as mixer blades or cutting tools are in contact with granular matter. Contacts with individual particles generate contact forces that act on both the engineering device and the granular material. The latter experiences a displacement of individual particles whereby the engineering structure responds with deformation and stresses. In order to predict and optimise both the behaviour and motion of granular material and the structures in contact, numerical simulation tools are increasingly employed. Simulations are popular especially because experiments are often expensive, time-consuming and sometimes even dangerous. The continuous increase in computing power is now enabling researchers to implement numerical methods that do not focus on the granular assembly as an entity, but rather deduce its global characteristics from observing the individual behaviour of each grain. An interaction between granular media and a structure relies on a transfer of forces between them. Granular media consists of an ensemble of particles of which a number of particles may be in contact with a surface e.g. walls as surfaces of solid structures. The contact is resolved similar to inter-particle contacts by a representative overlap. It defines the position of impact as well as the force acting on the particle at this position. The same force, however, in the opposite direction defines a mechanical load for the structure. In order to determine the effect of forces on the solid structure, it is discretised using finite elements. The impact of the force is transferred to the nodes

A non-invasive experimental method and a clustering DEM model were developed in this study to investigate micro-macro behaviors of real granular materials with irregular particle shape configurations. The investigated behaviors include global deformations, failure strengths and residual strengths, stress and strain distributions, local coordination number, local void ratio, particle kinematics, and fabric orientation distributions. The experimental method includes an approach to automatically identify and recognize multiple particles using x-ray computed tomography imaging (XCT) and an enhanced approach to digitally represent microstructures of granular materials. The digitally represented microstructure can be directly employed for numerical simulation setup. A compression test and a direct shear test on coarse aggregates were conducted and analyzed using this method. The experimental measurements were applied for the evaluation of DEM simulations. The clustering DEM model provided in this study extends the conventional DEM model by incorporating actual microstructure of materials into simulations. Real irregular particles were represented by clusters of balls in the clustering DEM model while spherical particles were employed in the conventional DEM model. The PFC3D commercial software was applied for 3D DEM simulations of the compression test and the direct shear test. Compared to the conventional DEM model, the clustering DEM model demonstrated a better capability of predicting both the micro and macro behaviors of granular materials, including dilation, strength, particle kinematics, and fabric evolution. Fabric distribution was investigated for both the conventional DEM model and the clustering DEM model. The clustering DEM model described the fabric distribution of actual materials more precisely. This feature enabled it to simulate micro-macro behaviors of materials more accurately. A theoretic stress-fabric tensor relationship was also evaluated using the simulated stress and fabric distributions based on the actual microstructure of a real material. This relationship incorporated the anisotropic microstructure characteristics of the material. Whether it can better describe behaviors of granular materials was evaluated in this study. Generally, this research provides a more inherent understanding of granular materials through both DEM simulations and experimental validations.

This paper deals with the mechanical behaviour, especially the permanent deformation and resilient deformation of an unbound granular material (UGM) from Bréfauchet quarry which is used as base layer material in low traffic pavements for full-scale tests at IFSTTAR in France. Medium-scale repeated load triaxial tests (RLTT) are carried out at different water contents and the results show that both permanent and resilient deformations increase with water content. Besides, two techniques of fixing the sensors in materials with large particles for RLTTs are proposed and compared with each other. The results suggest that the tube method is more suitable for the UGM for an accurate measurement and a good adaptability is obtained during the RLTT. Based on the test results of UGM Bréfauchet, the modelling work is performed with improved models used previously for a sandy material. It appears that both the permanent and resilient behaviours of different unbound granular materials can be well captured by the proposed equations considering the effects of water content and anisotropy. This study is helpful to understand the evolution of permanent and resilient deformation in different granular layers, especially for the base layer, in low traffic pavements. The verified models can be used for other similar granular materials and this will lead to reducing the number of tests required to predict the deformation behaviour of granular materials.

A code based on the discrete element method (DEM) was developed to simulate the behaviour of angular granular materials by loading assemblies of two-dimensional polygon-shaped particles. Two series of test simulations—isotropic loading–unloading and biaxial shear—were conducted on assemblies with different particle angularity. To avoid the probable effect of particle eccentricity and size distribution on assembly behaviour, equal-sized, equal-sided particles were employed. Six assemblies of particles with different angularities (one assembly for each type) were used in this study. The test results are presented in terms of macroscopic and microscopic behaviour. It was found that particle angularity had a significant influence on the behaviour of simulated granular material.

The geo-mechanical behavior of granular materials rigorously depends on their initial packing density, stress level and particle size distribution. Moreover, the behavior of binary granular soil is affected by the quality and quantity of their small particles named the fines content (FC). The contribution mechanism of the FC to the load-bearing structure of the soil at various particle sizes, stress levels and densities is still pending. The present study aimed to use a micromechanical approach to simulate the behavior of binary mixtures with particle size ratios (α) of 2.5 to 7.1 and study the effect of stress level and initial packing density on the stress–strain behavior using discrete element method (DEM). Accordingly, the effect of FC on the internal friction angle, anisotropy parameters, coordination number and coarse–fine (C–F) contacts have been studied. The results indicate that the variation in peak shear strength versus FC is bell-shaped with a minimum for FC of 30% to 40% and this is independent of initial packing density and stress level, but depending on the value of α. The greater particle size ratios (α = 7.1) increase the tendency of fines particles to rotate during biaxial testing, reduced the shear strength in comparison with samples with small particle size ratios (α = 2.5). Exceeding the threshold FC (30–40%) led to formation of stronger force chains among the fines and increased the role of FC on the peak shear strength.

Investigations of the effects of particle morphology on granular material behaviors using a multi-sphere approach

This paper presents the discrete element method (DEM) simulations on the instability behaviour of granular materials during constant shear drained condition (CSD). CSD condition was implemented by decreasing mean effective stress on an assembly of particles under strain controlled loading. In this study, the instability condition was predicted at the particle scale level using particle second order work increment (Nicot et al. in Int J Solids Struct 49(10):1252–1258, 2012). The DEM contact parameters have been calibrated to capture the macroscopic responses and the instability behaviour consistently with the laboratory experiments. The effect of different range of initial states at the beginning of CSD condition such as different initial mean effective stress ( $$p_{0}^{^{\prime}}$$ ), void ratio ( $$e_{0}$$ ) and deviatoric stress ( $$q$$ ) on the instability behaviour were analysed. In addition, the micromechanical parameters such as coordination number, anisotropic coefficients (geometric, mechanical) have been extracted to assist in characterising the instability behaviour during CSD condition. The initial stress state of the soil (i.e. at the onset of CSD) has shown a significant influence on the evolution of anisotropic coefficients. An increase in geometric anisotropy and a decrease in mechanical anisotropy with time was observed after the instability.

Granular materials are extensively used throughout many industries. In countries like Australia and South Africa, national economies are critically dependent on the agricultural and mining industries, and it is important to understand bulk material behaviour in order to handle these materials properly. There are many diverse approaches to modelling granular materials. In this thesis, the Coulomb-Mohr continuum mechanical theory of granular materials is utilised, and some exact analytical solutions are presented for both stress and velocity fields. These solutions are formally valid provided sin φ = 1, where φ is the angle of internal friction, and they provide limiting solutions for so called highly frictional granular materials, for which sin φ ≈ 1. The solutions so obtained are exploited for three real industrial granular problems, namely gravity flow from converging hoppers, the stress distribution in stockpiles and finally, the stress distribution within rat-holes. The flow of granular materials, in the presence of gravity, through a converging hopper is an important problem that occurs in many industrial processes. Here, for highly frictional granular materials for both wedge and conical hopper flows, exact analytical solutions are obtained to determine the stress and velocity fields within the neighborhood of the hopper outlet. For the same problem, these exact solutions are exploited as the leading order terms in a regular perturbation series, where the correction terms are of order 1− sin φ. In this way, approximate analytical solutions are obtained that can be used to describe the behaviour of more realistic granular materials. The practice of storing granular materials in stockpiles occurs throughout the ii world in many industrial situations. In this thesis, exact solutions for highly frictional granular materials are used for the determination of the stress distributions within two-dimensional and axially symmetric stockpiles. Stockpile profiles considered here include the standard wedge and cone, as well as two-dimensional parabolic and axially symmetric cubic curved shaped stockpiles. We emphasise that curved stockpiles have not previously been considered in the literature. Our model assumes that the stockpile is composed of two regions, namely an inner rigid region and an outer yield region. The exact solution applies in the outer yield region, which is then extended continuously into the inner rigid region. A rat-hole is the general term used to describe those stable cavities, which frequently occur in storage hoppers and stockpiles, whose formation prevents further material falling through the outlet. In this thesis, we present exact solutions for both two-dimensional and axially symmetric rat-holes, where it is assumed that the highly frictional granular material has flowed through a central outlet, until the point is reached when there is no further flow of material. The remaining material is assumed to be in limiting equilibrium, that is static but on the point of yield. In both two dimensions and axial symmetry, two types of rat-holes are studied. The first type has a sloping upper surface of infinite extent, where the material is resting on a sloping rigid base containing an infinitesimal central outlet. The second type has a curved upper surface, where the material is resting between vertical walls and a horizontal rigid plane containing an infinitesimal central outlet. Again, we emphasise that neither of these rat-hole problems have previously been investigated in the literature.

Vibration has been widely used in various industrial operations dealing with granular materials. Classification, conveying and packing provide typical examples of the vibration technique. In spite of these actual uses, the behaviour of granular materials is poorly understood. Most of the knowledge related to handling of particulates is empirical and no generalized approach for the analysis of the response of granular materials to external forces exists. This paper presents an investigation into the development of a numerical method for size segregation, which is the typical behavior of granular materials in the field of vibration. This numerical method is modified on the basis of the discrete element method proposed by Cundall. In order to consider the shape anisotropy of particles, they are first treated as elliptic models. Then mechanical units such as spring, dashpots and friction sliders are used to express the contact forces. The effect of the size ratio and the shape of each particle on the response of granular materials is considered.

The discrete-element method (DEM) has gained popularity for developing a qualitative understanding of soil behaviour under a critical state soil mechanics (CSSM) framework. Most studies with a three-dimensional assembly of particles have used spheres as representative granular material to reduce computational demands. However, most granular materials – for example, sands – are not rounded, but possess features of angularity. Therefore, ellipsoid and cluster particles with different degrees of eccentricity were used in this study to evaluate the effect of the particle shape on the drained and undrained triaxial loading behaviour after isotropic and K0 consolidation. The particle numerical properties and grain size distributions were kept the same for all specimens, irrespective of particle shape. The critical state data points for spheres and ellipsoids plotted on almost the same critical state line (CSL) in e–log(p′) space, whereas the CSLs of clusters plotted above them. Additionally, M lines shifted downward with increasing sphericity. It was also found that the stress ratio at the triggering of static liquefaction (ηIS = q/p′) in ηIS–ψ space was affected by particle shape and consolidation path. The dilatancy (d = dεvp/dεqp) was also affected by particle shape. It was found that dilatancy parameters for the SANISAND constitutive model are affected by particle shape, which may contribute to an improved understanding of particle shape in constitutive modelling.

Effect of particle type on the shear behaviour of granular materials