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A constitutive model has been developed to capture the behavior of cross-anisotropic frictional materials. The elastoplastic, single hardening model for isotropic materials serves as the basic framework. Based on the experimental results of cross-anisotropic sands in isotropic compression tests, the principal stress coordinate system is rotated such that the model operates isotropically within the rotated framework. Experimental plastic work contours on the octahedral plane are plotted for a series of true triaxial tests on dense Santa Monica Beach sand to study the effects of cross anisotropy on the evolution of yield surfaces. The amount of rotation of the yield and plastic potential surfaces decreases to zero (isotropic state) with loading. The model is constructed for cases where the principal stress and material symmetry axes are collinear and no significant rotation of principal stresses occur. The model incorporates fourteen parameters that can be determined from simple experiments, such as isotropic compression, drained triaxial compression, and triaxial extension tests. A series of true triaxial and isotropic compression tests on dense Santa Monica Beach sand are used as a basis for verification of the capabilities of the proposed model. CE Database subject headings: Granular materials; Anisotropy; Isotropic materials; Compression tests; Triaxial tests; Models.

This paper presents a sensitivity analysis of the input parameters of a program based on the discrete element method (DEM). Triaxial compression simulations were conducted on an assembly of ellipsoids with two particle shapes. We examine four input parameters including shear modulus of particles, density of particles, time step, and damping. Generally, these parameters are chosen by calibrating the result with certain known behavior of granular materials. In dynamic simulations, these input parameters are bounded by their physical attributions that should not be altered. However, in static simulations, they do not have the same physical implication. Validity of results may be questionable when input parameters are used without justification. A sensitivity analysis of the input parameters should shed light on this issue. In this paper, we will study the effect of the input values within the range of (1/10)-10 times the benchmark value. The benchmark values are commonly used by the writer. The results are presented against the benchmark simulation. The unbalanced forces in the simulations are kept below a prescribed value to enforce equilibrium. The result shows that the effect of all input parameters used in this paper is negligible as long as the small unbalanced forces in the system can be achieved. The runtimes are different. However, there are two simulations (one with low damping and the other with a large time step size) that cannot maintain the required small unbalanced force. In other words, equilibrium cannot be achieved for these simulations. CE Database subject headings: Granular materials; Discrete elements; Triaxial Compression; Micromechanics

Rotation of particles in granular material is an important mechanism, which is responsible for the distinct feature of moment transfer within granular material. A couple-stress continuum is adopted to model such effect. The paper presents a mix-mode finite element formulation for the analysis of a couple stress continuum. A modified variational formulation is proposed to render unconditional convergence. The developed finite element method is validated by comparing the computed results with closed-form solutions. In order to verify whether the couple-stress continuum is appropriate for modeling granular media, finite element results for two different boundary value problems are performed and compared with that obtained from discrete analysis. Physical meaning of internal length, a new parameter of the material, is discussed. The suitability of the couple-stress continuum for modeling granular medium is evaluated. CE Database subject headings: Granular materials; finite element method; Bonding; Elastic analysis; Deformation analysis; Stress distribution; Numerical models; Two-dimensional analysis.

An experimental study on granular materials in triaxial extension at confining pressures from 0.25 to 68 MPa is presented. Drained and undrained tests were performed utilizing cylindrical specimens. Strain localization was repeatedly encountered in the form of specimen necking. The strain localization was determined to initiate very early in the test. The cause of the strain localization was determined to be the inherent instability in the axisymmetric extension test, which allows stresses, and therefore deformations, to concentrate at the weakest part of the specimen. This instability is a result of the inward radial strains experienced during the extension test. The effect is to lower the measured failure stresses and strains resulting in the conclusion that the conventional extension test is unreliable for determining soil strength in extension. A method was developed to enforce uniform strains in triaxial extension tests on cylindrical specimens by the use of small metal plates separated by lubricated latex membranes. Using this method a series of uniform-strain tests were performed. Detailed comparisons between strain-localized and uniform-strain tests are presented.

: Two-dimensional particles experience shear bands as real granular materials; they form a convenient vehicle to investigate shear bands within granular soils. Numerical simulations on these idealized materials are used to assess the assumptions and limitations of the shear-band analyses that are based on linear stability theory and micropolar continua. These shear-band analyses are found to be applicable in the postbifurcation range, and they describe the thickness of shear bands and the displacements and rotations of the particles within the shear bands of idealized granular materials. The influence of particle rotation within shear bands validates the use of micropolar models. The thickness of shear bands is strongly influenced by the model parameters controlling the micropolar effects. The constitutive models based on the deformation and flow theories of plasticity predict similarly the emergence and inclination of shear bands, but give different shear-band thicknesses., Numerical simulations of two-dimensional particles in granular soils are used to analyzed assumptions and limitations of the shear-band analyses based on linear stability theory and micropolar models. A model based on the deformation theory of plasticity is used to analyze the displacement and rotation of the particles in shear bands. Shear band thickness is affected by model parameters that control micropolar effects and different thicknesses are obtained using models based on the deformation and flow theories of plasticity.

A distinct element analysis of the behavior of a granular material was performed by simulating direct shear tests of a dense and a loose 2D sample of 1,050 cylinders. Macroscopic results exhibit typical features of the shear response of granular materials: a perfect plasticity state that does not depend on the initial density, a peak stress and a dilatant behavior in the case of the dense sample, and a contractant behavior of the loose sample. A micromechanical analysis of the shear behavior was carried out based on the simulation results. Using the particle displacements and rotations, a shear band is located within the sample. Special attention is focused on the evolution of particle/particle contact orientation as well as on the direction of particle/particle contact forces. The shear process induces a clear change of contact and contact force orientations. A strong correlation between the induced anisotropy of the microstructure and the macroscopic loading is evident in the simulation results.

A detailed nonlinear finite-element analysis is undertaken of the wall pressures exerted by iron ore pellets in a full-scale silo experiment. The ring stiffeners on the exterior of the silo wall cause local small axisymmetric geometric imperfections, and the effect of these on the pressure predictions is explored, together with its sensitivity to the chosen bulk solid constitutive model. This paper focuses on the filling pressures alone, because these are a necessary starting point if discharge pressure predictions are to be made with confidence.

Some important numerical aspects concerning the finite-element simulation of granular flow are presented. The main topic of this paper is the so-called 'switch' phenomenon, which is a stress peak at the junction of the vertical and the inclined part of a mass flow silo during its discharge. Case studies prove that the FE simulation of silos and simplified systems should be handled with great care, as many wall pressure peaks occurring at places where the shape of the silo is changing may well be caused by numerical corner singularities. Other numerical aspects lead to consequences for the filling process and the opening phase of silo emptying.

The most demanding design situations for silo structures usually occur at the onset of discharge, when the silo is still almost full of granular solid. In this condition, the pattern of solids flow affects the wall pressures, and both are currently difficult to predict even using the best numerical models. This paper describes part of an international collaborative study in which finite element and discrete element models were used by many leading research groups around the world to model a single well-defined problem of discharge from a flat-bottomed silo using many different programs. The results show that discrete element models give good qualitative predictions of flow patterns, and the finite-element models give good quantitative predictions of pressure regimes, but there is little agreement on the details either within each modeling paradigm or between them. Further extensive research is needed to reach a scientific consensus on the requirements for a reliable formulation.

Granular dynamics simulations of a 2D heap formation have been carried out at low- and high-impact feed rates for a 3:1 diameter ratio binary mixture. The data have been analyzed using novel time series and filtering analysis to investigate key representative many-particle dynamic events of the assembly evolution. Spectral analysis of the time series has revealed quite different periodic behavior in the low- and high-impact cases. Segregation occurs in the low-impact case whereas more uniform mixing of the two types of particles arises at high impact, which is consistent with previous experimental observations. The low-impact feed regime is shown to be characterized by discrete surface avalanching manifesting kinetic sieving of the finer particles, in which the large particles move preferentially toward the free surface and segregate in the boundary layer on rolling toward the horizontal base. In contrast, the high-impact feed regime is marked by periodic lateral surging and vertical 'pluming' of particles from below toward the free surface.

A granular medium is viewed as a heterogeneous continuum that satisfies mechanical equilibrium at each material point. Analysis of the strain distribution under deviatoric loading displays structures formation when the strain pattern is filtered through a directionally sensitive deformation intensity analyzer. The same type of analysis carried out on numerical experiments yields similar structures. Comparison between the two methods permits an estimate of the radius of the mesodomain that is characteristic for granular media. This scale is one of the necessary scales of discrimination that is needed for the understanding of the deformation of granular materials with elastofrictional particle interaction. Evolution of the thickness of the structures is also analyzed. They become elongated with increasing deviatoric deformation. The encroachment of the mesoscale onto the microscale (that is, the particle interactive scale) is signaled.