Inter-particle Friction Angle Research Articles

Normalized shear modulus reduction and damping ratio curves of quartz sand and rhyolitic crushed rock

This paper presents a laboratory investigation of the strain-dependent dynamic properties of volcanic granular soils composed of a rhyolitic crushed rock along with additional experiments on quartz sand through a high-amplitude resonant column testing program. The sands were tested in a dry state in torsional mode of vibration and thus the degradation of the normalized shear modulus and the increase of damping ratio in shear as a function of the shear strain amplitude (γ) were examined. It was revealed that, for a given mean effective confining pressure (σm') and coefficient of uniformity (Cu), the volcanic sands showed higher linearity in comparison to the quartz sands and that this trend became more pronounced with decreasing σm' and increasing Cu. In contrast to the general trend observed in the quartz soils, the confining pressure and the grain-size characteristics hardly affected the rate of normalized modulus degradation and damping increase in the volcanic sands. These differences are possibly related to the micro-mechanisms that dominate at particle contacts in the range of small to medium shear strain amplitudes. For example, the possible more pronounced crushing of the asperities during the elevation of the confining pressure and during the dynamic loading along with the lower inter-particle friction angle and stiffness of the volcanic sands of crushable particles in comparison to the quartz sands of stronger particles might play an important role in the energy dissipation during the dynamic excitation and thus on the rate of damping increase or modulus degradation.

Simulation of triaxial compression tests with polyhedral discrete elements

The triaxial compression test is by far the most common laboratory test used to measure the mechanical properties of granular soils. In this paper, a series of simulations using the discrete element method (DEM) with polyhedral particles are introduced to simulate drained and undrained triaxial compression tests. A series of DEM simulations are first presented to replicate nine isotropically consolidated drained triaxial compression (CIDC) tests on sand specimens. The DEM micro-mechanical parameters of the inter-particle friction angle, normal and shear contact stiffness were calibrated using a single test in the series. The calibrated DEM model was then used to compute the response of other eight tests. The model gave very good estimate of the behavior for the other eight tests corresponding to a range of initial void ratios and confining pressures. The deviatoric stress and volumetric strains obtained in each CIDC test simulation show good agreement with the corresponding experimental data. The major source of error in the simulations is the use of larger particle sizes necessary to keep the computational cost manageable. The DEM model was then used to compute undrained response of the sand specimens by simulating isotropically consolidated undrained triaxial compression (CIUC) tests. The computed responses, presented in terms of the stress path, deviatoric stress, and shear induced pore water pressure, are consistent with our understanding of sand behavior. The simulations demonstrate that polyhedral DEM provides a suitable tool for representing granular material responses in triaxial shear without the need for use of complex input model parameters.

Effect of Interparticle Friction on the Cyclic Behavior of Granular Materials Using 2D DEM

This study presents the influence of the interparticle friction angle on the cyclic behavior of granular materials using the two-dimensional (2D) discrete-element method (DEM). The numerical sample was modeled with oval-shaped particles, whereas the isotropically compressed dense sample was prepared from the initial sparse sample using periodic boundaries. Biaxial cyclic shear tests were simulated with different interparticle friction angles. It was noted that the width of the stress-strain cyclic loops becomes thin when the interparticle friction angle increases. It was also noted that the induced fabric anisotropy is more pronounced during unloading than loading. Moreover, a strong correlation between macro- and microquantities was observed for strong contacts during cyclic loading.

Critical State of Granular Materials Based on the Sliding-Rolling Theory

By representing the assembly by a simplified column model, a constitutive theory was recently developed for a two-dimensional assembly of rods. This theory, referred to as the sliding-rolling theory, is extended in this paper to represent the triaxial stress-strain behavior of granular materials. The sliding-rolling theory provides a dilatancy rule and an expression for the slope of the line of zero dilatancy in the stress space. These rules are then combined with triaxial observations to provide a microstructural interpretation of the critical state of granular materials. According to the theory, the slope of the critical state line in the stress space depends on the interparticle friction angle and the degree of contact normal anisotropy. To verify the basic ideas of the sliding-rolling theory, numerical experiments are conducted using the discrete-element method on three-dimensional assemblies of spheres.

Simulating a direct shear box test by DEM

Distinct element simulation was performed for direct shear box (DSB) tests on a dense and a loose two-dimensional (2D) sample of 3259 cylinders. Special attention was devoted to the effect that the frictional force between the inside surface of the upper shear box and the sample had on the measured shear strength in the DSB test. Some ways of minimizing this interface frictional force were introduced in the paper. Given that the deformation approximates simple shear within the deforming zone across the sample centre (referred to as the shear zone), a method was proposed to evaluate the overall strains in the DSB test. The numerically simulated data were used to interpret, on a microscopic scale, the angle of internal friction and a 2D stress–dilatancy equation for the mobilized plane in granular material. It was found that the angle of internal friction in granular material is not directly related to the interparticle friction angle (ϕµ). Instead, it relates to the average interparticle contact angle ([Formula: see text]) on the mobilized plane and the ratio k/f0, representing the degree of the probability distribution of the interparticle contact forces that is biased toward the positive zone of the contact angle θ (along the shear direction), where k is the slope of the linear distribution of the average interparticle contact forces against the interparticle contact angle; and f0is the average interparticle contact force.Key words: angle of internal friction, direct shear box test, distinct element method, friction, granular material, stress–dilatancy.

Numerical modelling of plane strain tests on sands using a particulate approach

This paper describes the results of a series of numerical plane strain test simulations on a particulate material, carried out using the three-dimensional particle flow code PFC-3D. Samples comprised about 10 000 non-spherical particles, each formed by strongly bonding two spheres together. The simulations demonstrate the ability of such a model to capture the essential macro-features of soil behaviour as observed in laboratory tests, including the dependence of peak strengths on the initial void ratio relative to the critical. The development of strain localisations or shear bands associated with the use of rough loading platens, and the sensitivity of the model to the initial sample porosity, particle shape factor and interparticle friction angle, were also investigated.

Numerical modelling of plane strain tests on sands using a particulate approach

This paper describes the results of a series of numerical plane strain test simulations on a particulate material, carried out using the three-dimensional particle flow code PFC-3D. Samples comprised about 10 000 non-spherical particles, each formed by strongly bonding two spheres together. The simulations demonstrate the ability of such a model to capture the essential macro-features of soil behaviour as observed in laboratory tests, including the dependence of peak strengths on the initial void ratio relative to the critical. The development of strain localisations or shear bands associated with the use of rough loading platens, and the sensitivity of the model to the initial sample porosity, particle shape factor and interparticle friction angle, were also investigated.

A micromechanical study of rolling and sliding contacts in assemblies of oval granules

AbstractThe evolution of the microstructure of an assembly of cohesionless granular materials with associated pores, which carry the overall applied stresses through frictional contacts is a complex phenomenon. The macroscopic flow of such materials take place by the virtue of the relative rolling and sliding of the grains on the micro‐scale. A new discrete element method for biaxial compression simulations of random assemblies of oval particles with mixed sizes is introduced. During the course of deformation, the new positions of the grains are determined by employing the static equilibrium equations. A key aspect of the method is that, it is formulated for ellipse cross‐sectional particles, hence desirable inherent anisotropies are possible. A robust algorithm for the determination of the contact points between neighbouring grains is given. Employing the present methodology, many aspects of the behaviour of two‐dimensional assemblies of oval cross‐sectional rods have been successfully addressed. The effects of initial void ratio, interparticle friction angle, aspect ratio, and bedding angle on the rolling and sliding contacts are examined. The distribution of normals to the rolling and sliding contacts have different patterns and are concentrated along directions, which are approximately perpendicular to one another. On the other hand, the distribution of all contact normals (combined rolling and sliding) are close to that of rolling contacts, which confirm that rolling is the dominant mechanism. This phenomenon becomes more pronounced for higher intergranular friction angle. Characteristics of the rolling and sliding contacts are also discussed in the context of the force angle, which is the inclination of contact force with respect to the contact normal. Copyright © 2003 John Wiley & Sons, Ltd.

INFLUENCE OF PHYSICAL PROPERTIES OF SOLID-LIQUID PHASE ON DEBRIS FLOWS

The velocity and sediment concentration of sediment-water mixture flow change by the physical properties; e. g., mass density of solid and liquid phase, viscosity of liquid, interparticle friction angle of solid particle, etc. The laminar viscous term is introduced into the constitutive relations developed formerly by Egashira et al. to solve those. The effects of physical properties of solid and liquid phase on debris flow are investigated by means of experimental data as well as of numerical solutions for velocity profile, sediment concentration profile, flux sediment concentration and flow resistance. The results suggest that the present constitutive relations evaluate any changes of debris flow caused by physical properties of solid-liquid phase.

Yield and deformation of an assembly of disks subjected to a deviatoric stress loading

The deformation of an assembly of particles is examined using a discrete element method (DEM) numerical model. The particles are modeled as random-sized, rough, inelastic, circular two-dimensional disks. The simulations keep track of the displacements, velocities and contact forces of each particle in order to examine the local rearrangements of the particles during the deformation and to determine the bulk stress states. The behavior of cohesive materials can be examined by introducing tensile forces between particles. The tests are done by applying constant confining pressures on two parallel flexible boundaries and a constant displacement rate on the two other flat frictionless walls. During the loading, the axial stress on the moving walls reaches a peak value and afterwards remains essentially constant for large strains. Stress–strain curves are obtained for a large range of confining pressures. They show that the yield envelopes follow the linear Mohr–Coulomb criterion. The global angle of friction is determined for a large range of particle–particle friction angles and particle size distributions. It was found that the global friction angle φ cv increased with interparticle friction angle φ i for φ i<6°; for larger values of φ i, the global friction angle is essentially constant. As the spread in the particle size distribution increased, the magnitude of the internal angle of friction was found to increase for a given interparticle friction angle.

Observations on the effects of particle rotations on the failure of idealized granular materials

Based on the computer simulations of biaxial tests, particle rotations are shown to have little influence on the elastic properties of idealized granular materials, but significant effects on their shear strength. The overall peak and residual friction angles, ø p and ø r, are smaller than the interparticle friction angle ø μ because of the concentration of rotations in shear bands. When particle rotations are artificially prevented, ø p and ø r, become larger than ø μ and the localized failure patterns become different from those observed experimentally in granular media. The average particle rotation remains small in the complete biaxial specimen, but increases in shear bands. The particle rotations follow an exponential distribution independent of the axial strain. Particle rotations induce twice as many rolling contacts as sliding contacts. Compared to sliding contacts, rolling contacts are oriented differently, generate different fabric tensors, and are less capable of dissipating energy and supporting inclined contact forces.

Theory for Shear Strength of Granular Materials

Based on statistical methods, a theory has been proposed for the shear strength of a random assembly of spherical cohesionless particles. The theoretical analysis gives a relationship between angle of internal friction φ\dc\dv at constant volume, interparticle friction angle φ\Dμ\N, and void ratio e. For comparison, drained triaxial compression tests have been carried out on steel spheres, uniform sands, and glass ballotini of different sizes. When φ\Dμ\N is calculated from the experimentally obtained φ\dc\dv values it has been found that φ\Dμ\N is independent of void ratio, which is an indirect evidence to support the validity of the proposed theory. Comparison with experimental results on sands suggests that the use of the proposed theory could also be extended to random assemblies of irregular shaped particles as well.

On Stress-Dilatancy Relation of Sand In Simple Shear Test

A stress-dilatancy relation of sand is proposed on the basis of the experimental fact that the principal stress axes and the principal strain increment axes rotate without complete coincidence with each other during monotonous increace of horizontal shear stress acting on a sample in a simple shear test. The inclination angle φ of the major principal stress axis to the vertical direction is deduced from a simple relationship ; τ/σN = ĸ tan φ, which is derived from theoretical consideration (Oda and Konishi, 1974) and verified by Cole’s experimental results. The value of k is a material constant for a given sand which is dependent only on the interparticle friction angle. By using this relation, the principal stress parameters such as mean stress (σ1 + σ3) /2 and maximum shear stress (σ1 – σ3) /2 are easily deduced from the shear stress r and the normal stress acting on the horizontal shear plane in a simple shear test or even in a direct shear test.

An upper bound valve for the modified interparticle friction angle in the stress-dilatancy equation : 10F, 8R. Geotechnique, V24, N3, Sept. 1974, P269–287

An upper bound valve for the modified interparticle friction angle in the stress-dilatancy equation : 10F, 8R. Geotechnique, V24, N3, Sept. 1974, P269–287

Deformation Mechanism of Sand in Triaxial Compression Tests

Based on detailed observations by using a microscope and thin section method, a new granular model has been proposed as a basis of theoretical considerations on granular mechanics. The specimen deformed to residual stress state can be divided into three subdomains having each homogeneous fabric, i.e., dead domain, dilated domain and shear domain. The void ratio in the dilated domain becomes equal to 20% relative density at peak stress state whose value represents an unstable particle configuration in a granular material. Concentration of directions (Ni) perpendicular to tangential planes at contacts to the maximum principal stress direction performs an essential role in strengthening granular fabric up to the peak stress state. Relative movements between particles in the shear domain occur principally by preferred sliding along the contacts having Ni inclined to σ1-direction about 35°, and partially by rolling of each grain to reorient preferred dimensional orientation. Mobilized stress ratio of granular materials when subjected to a deviatoric stress state is found to depend not only upon the interparticle friction angle between grains ϕubut also upon the parameter representing fabric anisotropy Sz/Sx. Experiments on two kinds of sand show that theoretical equation is closely obeyed by experimental results throughout deformation to failure irrespective of their initial void ratio and initial fabric.