Microscopic study on stress-strain relation of granular materials (original) (raw)
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Granular Matter
The behavior of granular materials is very complex in nature and depends on particle shape, stress path, fabric, density, particle size distribution, amongst others. This paper presents a study of the effect of particle geometry (aspect ratio) on the mechanical behaviour of granular materials using the Discrete Element Method (DEM). This study discusses 3D DEM simulations of conventional triaxial and true triaxial tests. The numerical experiments employ samples with different particle aspect ratios and a unique particle size distribution (PSD). Test results show that both particle aspect ratio (AR) and intermediate stress ratio (b=(σ2'-σ3')/(σ1'-σ3')) affect the macroand micro-scale responses. At the macro-scale, the shear strength decreases with an increase in both aspect ratio and intermediate stress ratio b values. At the micro-scale level, the fabric evolution is also affected by both AR and b. The results from DEM analyses qualitatively agree with available experimental data. The critical state behaviour and failure states are also discussed. It is observed that the position of the critical state loci in the compression (e-p') space is only slightly affected by aspect ratio (AR) while the critical stress ratio is dependent on both AR and b. It is also demonstrated that the influence of the aspect ratio and the intermediate stress can be captured by micro-scale fabric evolutions that can be well understood within the framework of existing critical state theories. It is also found that for a given stress path, a unique critical state fabric norm is dependent on the particle shape but is independent of critical state void ratio.
Geotechnical and Geological Engineering, 2019
This study examines the macro-and micro-mechanical behaviors of granular materials at a low mean stress in general triaxial loading using the discrete element method. Spheres were used to model the particles to reduce the computational costs. They were placed in the grid points of a cube with their random values of diameters. The generated cubical sample was compressed isotropically with periodic boundaries to reach the target mean stress of 25 kPa. The isotropically compressed dense sample prepared in this way was subjected to shear by varying a nondimensional parameter, b ¼ ðr 0 2 À r 0 3 Þ=ðr 0 1 À r 0 3 Þ from 0 to 1. From the numerical study, it is observed that the simulated macro-results agree well with the experimental results. The evolution of principal stress and strain components and angle of shearing resistance is strongly dependent on b. However, the evolution of coordination number and slip coordination is not a function of b. The evolution of the components of contact fabric tensor considering the strong contacts has excellent similarity with that of stress components. The ratio of strong contact to total contact strongly depends on the values of b and it decreases at small strain level regardless of b and starts accumulating afterward as the strain increases.
Modelling and Simulation of Rate-Dependent Stress-Strain Behaviour of Granular Materials in Shear
Soils and Foundations, 2008
A constitutive modelling of the elasto-viscoplastic stress-strain behaviour of geomaterials in shear that has been developed within a non-linear three-component model framework is validated by simulating a comprehensive series of drained triaxial compression (TC) and direct shear (DS) tests on a wide variety of granular materials. Illustrative simulations of rate-dependent stress-strain behaviour of geomaterial under typical laboratory test conditions were performed to analyse the structure of the model. The versatility of the proposed model and its applicability to a wide variety of shear loading histories is examined and demonstrated by these simulations. The following results are shown. Commonly with diŠerent basic viscosity types, Isotach, TESRA and P&N, the viscous stress component has a positive component that increases with an increase in the irreversible strain rate, which makes feasible stable and realistic simulations of rate-dependent stress-strain behaviour, including creep deformation, based on the proposed model. With diŠerent unbound granular material types having similar relative densities, the creep strain in TC tests and creep shear displacement in DS tests that develop by sustained loading at a given shear stress level for a given period tends to decrease with an increase in the particle roundness. This trend of behaviours is explained by a decrease in the viscosity type parameter, u, associated with an increase in the particle roundness based on the simulations of these tests.
Effect of Particle Size on the Shear Strength Behavior of Granular Materials
During plastic deformation of granular materials due to loading, the stress-strain and strength characteristics of sand grains are influenced with grain size, their distribution and packing. Also the macroscopic behaviour of granular materials changes with the variation of microscopic behaviour. Particle size is one of the important properties which plays a dominant role on the stress, strain and strength responses of granular materials. Alteration of grain size results in the change of void ratio as well as particle effective contact area revolutionized and the load distribution mechanism of particle to particle contact. To evaluate the effect of particle size, a series of direct shear tests were performed considering uniform particles of eight samples (0.075, 0.15, 0.212, 0.300, 0.600, 1.18, 1.72 and 2.76 mm) and graded particles of two samples (0.075-1.18 mm and 0.075-2.36 mm). Three types of normal loads (0.05, 0.10 and 0.15 kN) were selected for each test. For uniform particles, particles retained on individual sieve size were considered and in graded particles combination of each uniform particle pondered. A theoretical approach was also proposed to correlate the particle size and macroscopic response. From the experimental results it was observed that for each set of normal load with the increase of particle size, angle of internal friction as well as maximum horizontal shear stress increases for uniform sands and a similar response was noticed in graded sands but the larger the gradation the higher the shear strength. Maximum horizontal shear and angle of internal friction with respect to particle size is also influenced by normal stress. Experimental results have good agreement with the theoretical approach.
Behavior of Sheared Granular Materials at Micro-Scale during the Cyclic Loading
Journal of Advanced Engineering and Computation
The aim of this paper is to explore the evolution of different micro-scale quantities during the cyclic loading using the discrete element method (DEM) for a granulate system such as sand. The numerical samples comprising of 9826 spheres were generated and consolidated isotropically using the periodic boundaries. These numerical samples were subjected to the cyclic loading for different maximum applied strains. The simulated stress-strain behavior was validated with the experiment and found an excellent agreement between them during loading and unloading. The evolutions of different micro-scale quantities were investigated in detail considering the variation of the maximum applied strain and the density of sample. It is noted that the evolution of the coordination number and the slip coordination number is a function of the maximum applied strain and the density of sample during the cyclic loading. The change of the slip coordination number is larger at the end of unloading than that a...
2004
The paper examines the evolution of microstructure and contact forces in a two-dimensional analogue granular material consisting of photoelastic disks under various loading paths. Several stress (strain) paths together with stress (strain) probes are performed in the context of biaxial element tests, and the resulting strain (stress) response envelopes are determined. This is a more objective way of evaluating the stressstrain behaviour of granular soils with reference to anisotropy and dilatancy. One of the findings of this investigation is the elucidation of the microstructural changes accompanying the instability behaviour of granular materials when all effective stresses nullify such as in static liquefaction. It is found that strong force chains develop in a dilating specimen, and that a flow type of failure is due to the buckling of these force chains. Instability is also more formally analyzed within the framework of Hill’s second order work. It is interesting to note that ex...
Finite Elements in Analysis and Design, 2008
In this paper a three-dimensional Discrete Element Method (DEM) is used to model cohesionless granular materials. Two different microscopic constitutive equations are used to resolve the contacts between single particles in the DEM: First, a simple penalty type contact law and second, a more sophisticated Hertzian type contact law. Numerical tests in form of DEM simulations of a cuboid particle sample under compression and shearing are performed using both microscopic constitutive equations. The microscopic results of the DEM in terms of inter-particle contact forces and particle trajectories are transferred to macroscopic results in terms of stresses and strains by a homogenization approach. The macroscopic results are presented and compared for the different microscopic constitutive equations.
Micromechanical Formulation of the Yield Surface in the Plasticity of Granular Materials
Journal of Applied Mathematics, 2013
An equation is proposed to unify the yield surface of granular materials by incorporating the fabric and its evolution. In microlevel analysis by employing a Fourier series that was developed to model fabric, it is directly included in the strength of granular materials. Inherent anisotropy is defined as a noncoaxiality between deposition angle and principal compressive stress. Stressinduced anisotropy is defined by the degree of anisotropy and the major direction of the contact normals. The difference between samples which have the same density (or void ratio) but different bedding angles is attributed to this equation. The validity of the formulation is verified by comparison with experimental data.
International Journal for Numerical and Analytical Methods in Geomechanics, 2003
This paper analyses the influence of grain shape and angularity on the behaviour of granular materials from a two-dimensional analysis by means of a discrete element method (Contact Dynamics). Different shapes of grains have been studied (circular, isotropic polygonal and elongated polygonal shapes) as well as different initial states (density) and directions of loading with respect to the initial fabric. Simulations of biaxial tests clearly show that the behaviour of samples with isotropic particles can be dissociated from that of samples with anisotropic particles. Indeed, for isotropic particles, angularity just tends to strengthen the behaviour of samples and slow down either local or global phenomena. One of the main results concerns the existence of a critical state for isotropic grains characterized by an angle of friction at the critical state, a critical void ratio and also a critical anisotropy. This critical state seems meaningless for elongated grains and the behaviour of samples generated with such particles is highly dependent on the direction of loading with respect to the initial fabric. The study of local variables related to fabric and particle orientation gives more information. In particular, the coincidence of the principal axes of the fabric tensor with those of the stress tensor is sudden for isotropic particles. On the contrary, this process is gradually initiated for elongated particles.
Stress-stress modelling for heterogeneous granular materials based on micromechanics
1995
The objective of this research is to develop a micromechanics theory for granular material considering the effects of micro-structure. This type of micro-structural based constitutive theory is useful in many fields of studies such as in the mechanics of soil, powder, composite and ceramic. The specific efforts are focused in the following four different areas: (1) descriptions of micro-structure, (2) micro-macro relationship, (3) classes of micromechanics constitutive theory, and (4) contact law of the inter-particle binder. These four areas are the fundamental elements to the construction of a micromechanics theory for granular media. Particular attention will be given to the effect of heterogeneity in micro-structure on the micro-macro mechanical behavior. The nature of this investigation is focused on theoretical development. The developed theory is evaluated by experimental and computer simulation results.