Strength Of Granular Materials Research Articles

An Enhanced Automated Particle Angularity Measurement Method

Abstract Angularity is an important aspect of particle morphology, directly correlated to the mechanical response and strength of granular materials. Many researchers have proposed multiple direct and indirect methods such as visual charts, analytical formulas, and advanced image-based techniques for qualitative and quantitative assessment of particle angularity, but no single method has been fully successful in distinguishing all types of particles and obtaining an accurate quantitative value of angularity. Nevertheless, because of the significant importance of the parameter, researchers have been using a few generally accepted angularity quantification methods. This paper evaluates the conceptual merits and demerits of four such methods, namely, two analog methods called “roundness index” and “degree of angularity” coined by Wadell and Lees, respectively, as well as two image-based methods called “angularity using outline slope” and “gradient angularity index” proposed by Rao, Tutumluer, and Kim and Chandan et al., respectively. The latter two methods were developed for use in conjunction with the University of Illinois Aggregate Image Analyzer and the Aggregate Imaging System, respectively. A new approach for angularity quantification is proposed herein based on insights from a rigorous analysis and critical assessment of these methods. The proposed method is compared against the existing methods based on Ward’s linkage method of clustering and is shown to be superior at distinguishing between various classes of particles. The proposed approach is demonstrated to be a better measure of the sharpness of the meso-level geometrical features of importance along a particle’s outline that are the controlling parameters contributing to particle angularity, which consequently correlates to the kinematic and mechanical response of granular materials.

DEM Modeling of Crushable Grain Material under Different Loading Conditions

This paper deals with the effect of contact conditions on the crushing mechanisms and the strength of granular materials. The computation of crushable grain material under different loading conditions is performed using 3D model of discrete element method (DEM). The crushable macro-grain is generated from a large number of identical spherical micro-grains which are connected according to the bonded particle model. First, the parameters of the proposed DEM model are calibrated to match the force-displacement curve obtained from Brazilian Tests performed on cylinders made of artificially crushable material. The damage profile right at the point when the force-displacement curve reaches its maximum is seen to replicate the same crack patterns observed in Brazilian test experiments. Then, parametric investigations are performed by varying the coordination number, the contact location distribution, and the contact area. The results show that these parameters play a significant role in determining the critical contact force and fracture mechanism of crushable particles compared to a traditional macro-grain crushing test. Increasing distribution and coordination number of the macro-grain increases particle strength when large area contact is permitted. However, for linear contact area, the effect of increasing coordination number on particle strength is marginal.

Failures in sand in reduced gravity environments

The strength of granular materials, specifically sand is important for understanding physical phenomena on other celestial bodies. However, relatively few experiments have been conducted to determine the dependence of strength properties on gravity. In this work, we experimentally investigated relative values of strength (the peak friction angle, the residual friction angle, the angle of repose, and the peak dilatancy angle) in Earth, Martian, Lunar, and near-zero gravity. The various angles were captured in a classical passive Earth pressure experiment conducted on board a reduced gravity flight and analyzed using digital image correlation. The data showed essentially no dependence of the peak friction angle on gravity, a decrease in the residual friction angle between Martian and Lunar gravity, no dependence of the angle of repose on gravity, and an increase in the dilation angle between Martian and Lunar gravity. Additionally, multiple flow surfaces were seen in near-zero gravity. These results highlight the importance of understanding strength and deformation mechanisms of granular materials at different levels of gravity.

On the stress-force-fabric equation in triaxial compressions: Some insights into the triaxial strength

The strength of granular materials during triaxial compression is investigated via a grain scale analysis in this paper. A 3D Discrete Element Method (DEM) program provides the triaxial strength data and helps to validate the micromechanical analysis. Some standard methods in statistics are employed first to quantitatively examine the assumptions made when deriving the stress-force-fabric (SFF) equation. After careful validation, a more concise format for the SFF equation is proposed for triaxial compressions. With this SFF equation, the strength is found to be jointly contributed by the magnitudes of the contact force anisotropy and fabric anisotropy. The influence of the initial void ratio, confining pressure and loading direction on the development of contact force anisotropy and fabric anisotropy is examined and presented. With similar techniques, the “force” term in the SFF equation is further decoupled, and an equation is obtained such that it explicitly links the contact force term with the friction coefficient between grains, a tensor defined as a statistic of the normal contact forces and a tensor defined as a statistic of the mobilisation status of contacts. Based on this equation, another equation regarding the stress ratio of granular assembly is obtained, and it clearly indicates two sources that contribute to the phenomenological friction nature of granular assembly. These two sources are caused by the contact force at the grain scale. The first is the anisotropy of the average normal contact forces, and the second is the mobilisation of contacts.

DEM Simulation of Biaxial Compression Experiments of Inherently Anisotropic Granular Materials and the Boundary Effects

The reliability of discrete element method (DEM) numerical simulations is significantly dependent on the particle-scale parameters and boundary conditions. To verify the DEM models, two series of biaxial compression tests on ellipse-shaped steel rods are used. The comparisons on the stress-strain relationship, strength, and deformation pattern of experiments and simulations indicate that the DEM models are able to capture the key macro- and micromechanical behavior of inherently anisotropic granular materials with high fidelity. By using the validated DEM models, the boundary effects on the macrodeformation, strain localization, and nonuniformity of stress distribution inside the specimens are investigated using two rigid boundaries and one flexible boundary. The results demonstrate that the boundary condition plays a significant role on the stress-strain relationship and strength of granular materials with inherent fabric anisotropy if the stresses are calculated by the force applied on the wall. However, the responses of the particle assembly measured inside the specimens are almost the same with little influence from the boundary conditions. The peak friction angle obtained from the compression tests with flexible boundary represents the real friction angle of particle assembly. Due to the weak lateral constraints, the degree of stress nonuniformity under flexible boundary is higher than that under rigid boundary.

Micromechanical Formulation of the Yield Surface in the Plasticity of Granular Materials

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. Stress-induced anisotropy is defined by the degree of anisotropy <svg style="vertical-align:-0.1638pt;width:9.7749996px;" id="M1" height="7.9499998" version="1.1" viewBox="0 0 9.7749996 7.9499998" width="9.7749996" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D6FC" d="M545 106q-67 -118 -134 -118q-24 0 -40 37.5t-30 129.5h-2q-47 -72 -103 -119.5t-108 -47.5q-47 0 -76 45.5t-29 119.5q0 113 85 204t174 91q47 0 70 -33.5t43 -119.5h3q32 47 80 140l55 13l10 -9q-47 -80 -138 -201q17 -99 27.5 -136t22.5 -37q23 0 69 61zM333 204&#xA;q-14 98 -31 149.5t-50 51.5q-49 0 -94 -70t-45 -164q0 -55 15.5 -86t40.5 -31q70 0 164 150z" /></g> </svg> 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.

The shear strength of granular materials containing dispersed oversized particles: DEM analysis

<p>Granular soils containing dispersed rock particles form part of many soil deposits. To obtain the shear strength of these mixtures, large representative samples need to be tested in either large triaxial or direct shear apparatuses. The use of this type of equipment makes the tests very time consuming and expensive. This study is designed to verify a theory of filler reinforcement presented by Guth (1945) that asserts that a mechanical property of a composite made of a mixture of a solid material reinforced by dispersed large particles (<i>p</i>^*) can be obtained from the related mechanical property, <i>p</i>, of the matrix, and the concentration by volume of the added dispersed oversized particles, <i>C_f</i>, if the following relationship is used: <i>p</i>^* = <i>p</i>(1 + 2.5 <i>C_f</i>). In this study, <i>p</i>^* represents the shear strength of a soil-rock mixture, <i>p</i> represents the shear strength of the soil matrix, and <i>C_f</i> as defined above. With the use of this relationship it is very easy to determine the shear strength of the mixture since one only needs to know the easily determinable quantities <i>p</i> and <i>C_f</i> in order to obtain <i>p</i>^*.</p><p>The validity of the relationship advanced by Guth (1945) was assessed using actual direct shear tests on sand with dispersed gravel, and direct shear test simulations that use the Discrete Element Method (DEM). The results of the actual direct shear tests were predicted very well by Guth's approach. The DEM simulations also validated it.</p>

Effect of rolling on dissipation in fault gouges

Sliding and rolling are two outstanding deformation modes in granular media. The first one induces frictional dissipation whereas the latter one involves deformation with negligible resistance. Using numerical simulations on two-dimensional shear cells, we investigate the effect of the grain rotation on the energy dissipation and the strength of granular materials under quasistatic shear deformation. Rolling and sliding are quantified in terms of the so-called Cosserat rotations. The observed spontaneous formation of vorticity cells and clusters of rotating bearings may provide an explanation for the long standing heat flow paradox of earthquake dynamics.

Strength of granular material in simple shear : Soils FoundV28, N2, June 1988, P85–94

Strength of granular material in simple shear : Soils FoundV28, N2, June 1988, P85–94

Strength of Granular Material in Simple Shear

ABSTRACT Investigated from a fundamental point of view is the strength of granular material in simple shear. The theoretical relation between the angle ϕs defined by tan ϕs = τ/σ and the angle ϕp defined by sin ϕp = (σ1 − σ2)/( σ1 + σ3) presents a useful information for engineering purpose. The theoretically derived relationship between the direction of major principal axis to the vertical ϕ and tan ϕs made clear that the expression of tan ϕs = κ tan ϕ (κ is a constant) is an approximate relation. The direction angle of the slip plane to the horizontal was also theoretically obtained. This angle is related to the difference between ϕs and ϕp and the slip plane never coincides with the horizontal at any instance. The relationship between ϕp and ϕs based on the author’s S model yields more realistic result than that based on the sliding block model. In this investigation, assumed is that the orientation of principal strain increment axis coincides with that of principal stress axis for the deformational regime after the most compactive point at which the positive dilatancy begins to take place.

Experimental micromechanical evaluation of strength of granular materials: Effects of particle rolling

Biaxial compression tests have been performed on assemblies of oval cross-sectional rods, in an effort to evaluate the effects of interparticle friction, particle shape, and initial fabric on the overall strength of granular materials. The variation in the spatial arrangement of the particles (fabric) and particle rolling and sliding are monitored by taking photoelastic pictures at various stages during the course of deformation. Based on this, the following conclusions are obtained. (1) Particle rolling appears to be a major microscopic deformation mechanism, especially when interparticle friction is large. (2) There are relatively few contacts at which relative sliding is dominant, and this seems to be true even when the assembly reaches the overall failure state; this observation is in contradiction to the common assumption that particle sliding is the major microscopic deformation mode. (3) During the course of deformation and up to the peak stress, new contacts are continually formed in such a manner that the contact unit normals tend to concentrate more in a direction parallel to the maximum principal compression. This concentration of unit normals seems to be closely related to the formation of new column-like load paths which carry the increasing axial stress under constant lateral force. After the peak stress, such a column-like microstructure disappears and considerable rearrangement of the load paths takes place, leading to a more diffused (homogeneous) microstructure in the critical state. (4) If a fabric tensor F ij , i, j = 1,2,3, is defined to be proportional to the volume average of the quantity m i m j , where m i are the rectangular Cartesian components of a unit vector along a vector that connects the centroids of two typical contacting granules, then it appears that the overall stress with components σ ij tends to become coaxial with the fabric tensor F ij , as the overall deformation continues. For two-dimensional granules the result σ ij = α O F ij + β O F jk F kj ( k summed) obtained by Mebrabadi, Nemat-Nasser and Oda (1980) by microchemical modeling is confirmed experimentally; α O and β O are material parameters.

Discussion of “Theory for Shear Strength of Granular Materials”

Discussion of “Theory for Shear Strength of Granular Materials”

Discussion of “Theory for Shear Strength of Granular Materials”

Discussion of “Theory for Shear Strength of Granular Materials”

The Drained Strength of Granular Material

Using the stress dilatancy relation R = DK, the drained strength of granular material is separated into its dilatant and frictional components. The factors influencing the value of 1 ≤ D ≤ 2 and Kμ ≤ K ≤ Kev are assessed theoretically, and experimental confirmation is provided from tests mainly on River Welland sand. These tests include five different sample geometries, and cell pressures up to 1000 p.s.i. (70.3 kg/cm2). The failure criterion is seen to be contained between two limiting types of behavior relevant to dense and loose assemblies. The main ambiguity exists in the case of axisymmetric extension when the strength is seen to be influenced by the sample boundary conditions.

Tensile Strength of Granular Materials

THE contribution by Carr1 on the tensile strength of granular materials raises two issues of fundamental importance: first, the validity of the equation for tensile strength proposed by Smalley and Smalley2 where B is the interparticle force per contact, D is the diameter of the particles and t is the thickness of the fracture zone; and secondly, the manner in which B varies with the degree of saturation. Equation 1 was derived on the assumption that fracture occurs on a plane normal to the tensile direction and that the particles intersected by this plane come apart without themselves contributing to the strength. For granular materials, where the bonding is provided by the capillary action of water, rupture of the particles is never possible.