Micromechanics Of Granular Materials Research Articles

The effect of consolidation on undrained behaviour of granular materials: experiment and DEM simulation

The characteristic features of undrained responses of granular materials, for example, stress ratio at instability ( η IS) and phase transformation ( η PT) states and the critical state (CS) behaviour, are often influenced by the consolidation history. However, there are limited studies in the literature, and a consensus has not yet been reached. This study combined the triaxial test of yellow silty sand and the three-dimensional discrete element method (DEM) simulation of ellipsoid particles under a triaxial condition to evaluate the effect of isotropic and K 0 consolidations. Triaxial test data formed non-unique CS lines (CSLs) in the e–log(p′) space for isotropic and K 0 tests, whereas the CSL was unique for DEM simulations; where e and p′ are the void ratio and mean effective stress, respectively. The micromechanical quantities, coordination number (C N) and fabric anisotropy (F vM) at the CS, also showed a unique relation with p′. The characteristic features, η IS and η PT, showed good correlation with the state parameter (ψ ) and the density indices. It was found that the η IS decreased with ψ, and the correlation was dependent on consolidation type. The micromechanical analysis suggested that F vM is a better parameter than C N to characterise the macromechanical behaviour. This study unambiguously supports the applicability of CS theory and provides insights into micromechanics of granular materials.

A micromechanical study of dilatancy of granular materials

In micromechanics of granular materials, relationships are investigated between micro-scale characteristics of particles and contacts and macro-scale, continuum characteristics. Dilatancy is an important property of granular materials, defined as volume changes (dilative or compressive) induced by shear deformation. To obtain detailed information at the micro-scale, two-dimensional Discrete Element Method simulations of isobaric tests with disk-shaped particles have been performed. The required information includes the fabric tensor which characterizes statistical properties of the contact network.The dependence of the dilatancy rate on the shear strength and the fabric tensor has been investigated, based on the results of the simulations employing a dense and a loose initial system. The dilatancy rate depends in a complex, non-unique way on the shear strength, while the dependence on the fabric tensor is more amenable to analytical description. Two micromechanical mechanisms of dilatancy have been identified: (i) dilatancy due to deformation of loops that are determined by the interparticle contact network and (ii) dilatancy due to topological changes in the interparticle contact network that correspond to the creation or disruption of contacts. For the first mechanism the anisotropy in the contact network is the primary parameter, while for the second mechanism the average number of contacts per particle is the primary parameter.A fabric-based micromechanical relation for the dilatancy rate has been formulated that describes these identified mechanisms. Parameters present in this relation are determined by fitting this relation to the results of the Discrete Element Method simulations, using combined data for the dense and the loose initial system. Employing these fitted coefficients, good agreement is obtained between the results of the simulations and the predictions of the micromechanical dilatancy relation.

Micromechanical study of elastic moduli of three-dimensional granular assemblies

In micromechanics of granular materials, relationships are investigated between micro-scale characteristics of particles and contacts and macro-scale continuum characteristics. For three-dimensional isotropic assemblies the macro-scale elastic characteristics are described by the bulk and the shear modulus, which depend on the micro-scale characteristics of the coordination number (i.e. the average number of contacts per particle) and the interparticle contact stiffnesses in directions normal and tangential to the contact.It is well-known that the uniform-strain theory (or mean-field theory) overpredicts the elastic moduli. To find improved predictions, approximations of the particle displacement and rotations fields are obtained here by solving the equilibrium equations for small subassemblies that are centred around particles. At the boundary of these subassemblies, the particle displacements and rotations are prescribed such that they conform to the mean field.Employing this approach, improved predictions of bulk and shear moduli are obtained, in comparison with those according to the uniform-strain assumption, especially when the size is increased of the subassemblies for which equilibrium equations are solved.The elastic moduli are evaluated from the particle displacement and rotations fields by two methods. In the first, stress-based method the micromechanical expression for the average stress tensor, in terms of the forces at contacts and the branch vectors that connect particles in contacts, is employed. In the second, energy-based method the minimum potential-energy principle is used to obtain rigorous upper bounds to the moduli. It is generally observed that the moduli obtained from the stress-based method give closer agreement with the results from Discrete Element Method simulations than those from the energy-based method.These improvements in the predictions of the elastic moduli are observed over the range of coordination numbers and interparticle stiffnesses considered here.

On the puzzling feature of the silence of precursory electromagnetic emissions

Abstract. It has been suggested that fracture-induced MHz–kHz electromagnetic emissions (EME), which emerge from a few days up to a few hours before the main seismic shock occurrence permit a real-time monitoring of the damage process during the last stages of earthquake preparation, as it happens at the laboratory scale. Despite fairly abundant evidence, electromagnetic (EM) precursors have not been adequately accepted as credible physical phenomena. These negative views are enhanced by the fact that certain "puzzling features" are repetitively observed in candidate fracture-induced pre-seismic EME. More precisely, EM silence in all frequency bands appears before the main seismic shock occurrence, as well as during the aftershock period. Actually, the view that "acceptance of "precursive" EM signals without convincing co-seismic signals should not be expected" seems to be reasonable. In this work we focus on this point. We examine whether the aforementioned features of EM silence are really puzzling ones or, instead, reflect well-documented characteristic features of the fracture process, in terms of universal structural patterns of the fracture process, recent laboratory experiments, numerical and theoretical studies of fracture dynamics, critical phenomena, percolation theory, and micromechanics of granular materials. Our analysis shows that these features should not be considered puzzling.

Influence of polydispersity on micromechanics of granular materials

We study the effect of polydispersity on the macroscopic physical properties of granular packings in two and three dimensions. A mean-field approach is developed to approximate the macroscale quantities as functions of the microscopic ones. We show that the trace of the fabric and stress tensors are proportional to the mean packing properties (e.g., packing fraction, average coordination number, and average normal force) and dimensionless correction factors, which depend only on the moments of the particle-size distribution. Similar results are obtained for the elements of the stiffness tensor of isotropic packings in the linear affine response regime. Our theoretical predictions are in good agreement with the simulation results.

Analysis of three-dimensional micro-mechanical strain formulations for granular materials: Evaluation of accuracy

An important objective of recent research on micro-mechanics of granular materials is to develop macroscopic constitutive relations in terms of micro-mechanical quantities at inter-particle contacts. Although the micro-mechanical formulation of the stress tensor is well established, the corresponding formulation for the strain tensor has proven to be much more evasive, still being the subject of much discussion. In this paper, we study various micro-mechanical strain formulations for three-dimensional granular assemblies, following the work of Bagi in two dimensions ( Bagi, 2006). All of these formulations are either based on an equivalent continuum approach, or follow the best-fit approach. Their accuracy is evaluated by comparing their results, using data from Discrete Element Method simulations on periodic assemblies, to the macroscopic deformation. It is found that Bagi’s formulation ( Bagi, 1996), which is based on the Delaunay tessellation of space, is the most accurate. Furthermore, the best-fit formulation based on particle displacements only did unexpectedly well, in contrast to previously reported results for two-dimensional assemblies.

Micromechanics of granular materials with capillary effects

Based on discrete element simulations and micromechanical calculations, this paper presents studies on the shear strength properties of unsaturated granular materials with capillary effects. Capillary forces are described on the local scale, depending on the water content, and are superimposed on the standard dry particle interaction that is currently described through an elastic–plastic relation. Simulations of triaxial compression tests at several water-content levels in the pendular regime are used to investigate the macroscopic consequences of this local description. The two methods are in rather good agreement, both reproducing the dependency of shear strength on water content, as classically observed in laboratory experiments. For the water-content levels considered, a nonlinear evolution of the cohesion with the water content is obtained, resulting in shear-strength saturation with increasing water content. Moreover, the computations allow a capillary stress tensor to be exhibited from capillary forces, directly related to the cohesion of the material. Finally, emphasising this capillary stress contribution, the generalised effective stress concept is reviewed, with a conclusion on the limitations of the classical macroscopic description of water effects in unsaturated granular materials.

A micromechanical model for the initial rearrangement stage of liquid phase sintering

A constitutive model for powders in the initial rearrangement stage of liquid phase sintering (LPS), where capillary force is the driving force for densification, is developed in this paper. The formulation is based on certain theories in micromechanics of granular materials (see Mehrabadi et al., 1992a; Mehrabadi et al., 1992b; Nemat-Nasser and Mehrabadi, 1983; Nemat-Nasser and Mehrabadi, 1984; Christoffersen et al., 1981). The anisotropic mechanical behavior of powder system is analyzed by considering the behavior of interparticle force and fabric which is represented by the distribution of contact normals. The proposed model is used to determine the dependence of the overall volume change on such factors as local liquid volume, uniformity of liquid distribution, contact angle, initial particle distance, initial confining pressure, particle size and viscosity. The numerical and theoretical analyses in this paper indicate that small particle size, small contact angle, low viscosity, even distribution of liquid phase and loose green powder mass enhance the amount of volume change in the initial stage of LPS. It is also found that a higher confining pressure increases the densification rate but it lowers the amount of net volume shrinkage at the end of the initial stage. The anisotropic behavior of the sample is analyzed by studying the interparticle force change and fabric change during the sintering.

Micromechanics of granular materials -numerical simulation of the effects of heterogeneities

Micromechanics of granular materials -numerical simulation of the effects of heterogeneities