Contact Force Anisotropy Research Articles

Compaction behavior of coarse-grained soil under various vibration frequencies: a DEM study

PurposeThis paper investigates the vibration compaction mechanism and evaluates the impact of vibration frequencies on the stability of coarse-grained soil, aiming to optimize the subgrade filling process.Design/methodology/approachThis study examines the vibratory compaction behavior of coarse-grained soils through indoor vibration tests and discrete element simulations. Focusing on angular gravel (breccias) of varying sizes, the simulations were calibrated using parameters such as Young’s modulus, restitution and friction coefficients. The analysis highlights how particle shape influences compaction, revealing mesoscopic mechanisms that drive macroscopic compaction outcomes.FindingsThis study investigates the influence of vibration frequency on the compaction behavior of coarse-grained soils using discrete element simulation. By analyzing particle contact and motion, the mesoscopic mechanisms driving compaction are explored. The study establishes a positive linear correlation between contact force anisotropy (Cv) and deformation, demonstrating that higher anisotropy leads to greater structural disruption. Additionally, the increase in sliding contact percentage (SCP) at higher frequencies indicates instability in the skeletal structure, driven by uneven contact force distribution. These findings reveal how frequency-induced stress concentration affects the stability and deformation of the soil skeleton.Originality/valueThis research explores the effect of various vibration frequencies on the compaction behavior of coarse-grained soils, examining microscopic interactions to reveal their impact on soil stability and deformation.

Micromechanical modeling of hollow cylinder torsional shear test on sand using discrete element method

Previous studies on the hollow cylinder torsional shear test (HCTST) have mainly focused on the macroscopic behavior, while the micromechanical responses in soil specimens with shaped particles have rarely been investigated. This paper develops a numerical model of the HCTST using the discrete element method (DEM). The method of bonded spheres in a hexagonal arrangement is proposed to generate flexible boundaries that can achieve real-time adjustment of the internal and external cell pressures and capture the inhomogeneous deformation in the radial direction during shearing. Representative angular particles are selected from Toyoura sand and reproduced in this model to approximate real sand particles. The model is then validated by comparing numerical and experimental results of HCTSTs on Toyoura sand with different major principal stress directions. Next, a series of HCTSTs with different combinations of major principal stress direction (α) and intermediate principal stress ratio (b) is simulated to quantitatively characterize the sand behavior under different shear conditions. The results show that the shaped particles are horizontally distributed before shearing, and the initial anisotropic packing structure further results in different stress–strain curves in cases with different α and b values. The distribution of force chains is affected by both α and b during the shear process, together with the formation of the shear bands in different patterns. The contact normal anisotropy and contact force anisotropy show different evolution patterns when either α or b varies, resulting in the differences in the non-coaxiality and other macroscopic responses. This study improves the understanding of the macroscopic response of sand from a microscopic perspective and provides valuable insights for the constitutive modeling of sand.

Exploring the role of particle-form polydispersity in the fabric of granular packing: Insights from DEM simulations with ellipsoidal particle assemblies

Granular materials, such as sand, exhibit a wide range of particle sizes and shapes, known as polydispersity. This study aims to investigate the effects of particle-form (first-level approximation of particle shape) polydispersity on a fabric of granular packing using DEM simulations of ellipsoidal particle assemblies. A framework for DEM simulations is proposed to investigate the particle-form polydispersity, and an overall polydispersity index (OPI) is introduced to quantify its magnitude. Various parameters are employed to quantify the fabric, including packing density, coordination number, contact force, and fabric anisotropy. The results highlight that the particle-form polydispersity notably affects the packing density and mean coordination number of the granular packings. Furthermore, a prediction model for the packing density and mean coordination number of polydisperse packings is proposed based on the correlations fitted from the monodisperse packing data.

Influence of particle shape on creep and stress relaxation behaviors of granular materials based on DEM

The creep and stress relaxation behaviors stem from time-dependent changes in the microstructure of granular materials. As a non-negligible inherent granular material characteristic, particle shape plays a significant role on the formation and evolution of microstructure. However, the effects of particle shape on creep and stress relaxation behaviors of granular materials are still open questions. In this study, 3D DEM models based on the rate process theory and superellipsoids are incorporated to simulate the creep and stress relaxation of granular samples with different aspect ratios and blockiness. The results show that the aspect ratio and blockiness of particle have a great effect on creep and stress relaxation. However, the effects of aspect ratio and blockiness on creep and stress relaxation are coupled. Further analysis on contact forces shows the influences of aspect ratio and blockiness on creep mainly come from the contact force ratio. The influences of the aspect ratio and blockiness on stress relaxation mainly arise from the variation of the normal contact force anisotropy of the granular assemblies. The above results provide the tendency and mechanism on the effects of particle shape on creep and stress relaxation of granular assemblies.

Study on Deformation Mechanism of Saturated Sand Based on Discrete Element Method

Based on the discrete element program (particle flow code PFC3D), the effects of the initial void ratio on the macroscopic and microscopic mechanical responses, phase transition state and critical state characteristics of saturated sand are systematically investigated in drained tests. The phenomenon that saturated sand enters the critical state earlier than the laboratory macroscopic results is revealed from the microscopic point of view. The results show that the phase transition state of the saturated sand can be reflected by the extreme values of void ratio, sliding ratio, suspended particle ratio and mechanical coordination number. Compared to the macroscopic parameters stress ratio and volume strain, the microscopic parameters can earlier reveal the critical state of saturated sand. The saturated sands with different initial void ratios have the same anisotropy component at the critical state. At the phase transition state, only the weight of normal contact force anisotropy is in the peak state. During the development of saturated sand from shrinkage to dilatancy, the velocity of particle motion on the diagonal 45° shear surface of the sample is intense and the particle motion is dominated by rotation. The above conclusions expand the current understanding of the deformation mechanism at the phase transition state and critical state of the soil.

Effect of rubber-sand particle size ratio on shear properties of rubber-sand mixtures under normal cyclic loading

The mechanical properties of rubber-sand mixtures are influenced by the ratio of rubber-sand particle sizes and the rubber content. Rubber-sand mixtures used as roadbed fillers are primarily subjected to normal cyclic traffic loading. Therefore, a series of direct shear tests on rubber-sand mixtures under normal cyclic loading were conducted using a large-scale direct shear apparatus. The effects of the rubber-sand particle size ratio, rubber content, initial stress, and amplitude of normal cyclic loading on the shear strength of rubber-sand mixtures were evaluated. Based on the indoor tests, discrete element models of rubber-sand mixtures with different particle size ratios were established to explore the meso-mechanical mechanism of the mixed soil during the direct shear process. The results indicate that rubber-sand mixtures with low rubber content and a particle size ratio >1 have a positive effect on the shear strength of the mixed soil. The impact of initial stress on the shear stress of the mixed soil is greater than that of the normal cyclic load amplitude. As the particle size ratio increases, the inter-particle contact force becomes larger, resulting in more noticeable group anisotropy. Additionally, the main direction of the normal contact force anisotropy in the mixture consistently aligns with the deflection direction of the force chain. Rubber particles in rubber-sand mixtures with a large particle size ratio actively participate in the contact force chain network system, facilitating load transfer and positively influencing shear strength.

Influence of the interparticle friction coefficient on the mechanical behaviour of breakable granular materials with realistic shape

Interparticle friction coefficient μ is an important factor affecting the mechanical properties of granular materials. In this study, the influence of μ on the mechanical behavior of granular materials is investigated by DEM. Through 3D scanning and Voronoi tessellations, the breakable particle model with realistic shape is constructed. A series of drained triaxial tests were performed at different μ values. Then, the particle breakage characteristics, including the degree of particle breakage and the breakage mode, were evaluated. In addition, microscopic characteristics, including coordination numbers and contact forces, were examined. Finally, the underlying mechanisms of φc evolution are explained from two perspectives of particle movement and fabric anisotropy. First, the rolling behavior of the particles increases with μ values, leading to a larger average displacement of particles. The influence of particle movement and friction coefficient balance each other, resulting in φc remaining constant when μ⩾0.4. Second, the initial increase of φc is due to the increase of the contact normal anisotropy ac, the normal contact force anisotropy an and the tangential contact force anisotropy at. Subsequently, the constant φc is the result of the decrease of ac and an being compensated by the increase of at.

Microscopic mechanical properties and fabric anisotropic evolution law of open graded gravel permeable base under dynamic loading

Under traffic dynamic load, the microscopic mechanical properties and the fabric anisotropic evolution of open graded gravel permeable base directly determine the ability of open graded gravel permeable base to resist external loads and maintain stability in service. Firstly, this article constructed a discrete element numerical model for open graded gravel permeable base, and verified the accuracy of the model through experiments. Then, the effects of gradation, nominal maximum particle size, friction coefficient between aggregate particles, and effective elastic modulus of aggregate on the microscopic mechanical properties, migration behavior, and the fabric anisotropic evolution of open graded gravel aggregate particles were studied in sequence. The research results indicate that the proposed image moving target tracking algorithm based on the three branches twin network can achieve precise tracking and measurement of particle microscopic migration behavior. The method proposed in this study for constructing a three-dimensional surface model of gravel particles based on the principle of multi view averaging and the scale invariant feature transformation algorithm can achieve rapid numerical reconstruction of the three-dimensional morphology of gravel particles at a low cost. The internal aggregate particles of intermediate grade gravel are more likely to form a stable network force chain topology structure that can effectively resist external loads. As the maximum nominal particle size increases, the topological structure of the contact force of gravel particles becomes sparse, and the proportion of strong contact force increases. Increasing the friction coefficient of the contact interface between aggregate particles can to some extent hinder the migration behavior of aggregate particles inside the graded gravel. As the effective elastic modulus of the aggregate increases, the internal network strong contact force chain topology of open graded gravel gradually forms. Under external loads, the migration speed and displacement of the aggregate particles inside open graded gravel decrease, and the degree of internal normal contact force and branch vector anisotropy also decrease.

DEM investigation of strain behaviour and force chain evolution of gravel–sand mixtures subjected to cyclic loading

The strain characteristic and load transmission of mixed granular matter are different from those of homogeneous granular matter. Cyclic loading renders the mechanical behaviours of mixed granular matter more complex. To investigate the dynamic responses of gravel–sand mixtures, the discrete element method (DEM) was used to simulate the cyclic loading of gravel–sand mixtures with low fines contents. Macroscopically, the evolution of the axial strain and volumetric strain was investigated. Mesoscopically, the coordination number and contact force anisotropy were studied, and the evolution of strong and weak contacts was explored from two dimensions of loading time and local space. The simulation results show that increasing fines content can accelerate the development of the axial strain and volumetric strain but has little effect on the evolution of contact forces. Strong contacts tend to develop along the loading boundary, presenting the spatial difference. Weak contacts are firstly controlled by confining pressure and then controlled by axial stress, while strong contacts are mainly controlled by axial stress throughout the whole cyclic loading. Once compression failure occurs, the release of axial stress causes the reduction of strong contact proportion in all local regions. These findings are helpful to understand the dynamic responses of gravel–sand mixtures, especially in deformation behaviours and the Spatio-temporal evolution of contact forces.

DEM simulation of the shear behaviour of breakable granular materials with various angularities

Particle shape is an important factor that affects particle breakage and the mechanical behaviour of granular materials. This report explored the effect of angularity on the mechanical behaviour of breakable granular materials under triaxial tests. Various angular particles are generated using the quasi-spherical polyhedron method. The angularity α is defined as the mean exterior angle of touching faces in a particle model. A breakable particle is constructed as an aggregate composed of coplanar and glued Voronoi polyhedra. After being prepared under the densest conditions, all assemblies were subjected to triaxial compression until a critical state was reached. The macroscopic characteristics, including the shear strength and dilatancy response, were investigated. Then, particle breakage characteristics, including the extent of particle breakage, breakage pattern and correlation between the particle breakage and energy input, were evaluated. Furthermore, the microscopic characteristics, including the contact force and fabric anisotropy, were examined to probe the microscopic origins of the shear strength. As α increases, the peak shear strength increases first and then remains constant, while the critical shear strength generally increases. Assemblies with larger angularity tend to cause more serious particle breakage. The relative breakage is linearly correlated with α under shear loading. Compared with unbreakable particles, the peak shear strength and the critical volumetric strain decline, and the degree of decline linearly increases with increasing α.

DEM exploration of confining stress effect in cyclic liquefaction of granular soils

Confining stress is a major consideration in the assessment of liquefaction resistance of granular soils. In this study, the influence of confining stress to cyclic liquefaction from micromechanical perspectives are explored using DEM simulations. Eight samples with different confining stresses and void ratios are prepared and subjected to undrained cyclic loading tests to reach initial liquefaction. It is observed that the influence of confining stress to coordination number of the sample before shearing is limited. However, confining stress has a significant influence to probability distribution of normal contact forces. Sample with higher confining stress has higher fraction of medium normal forces. During liquefaction process, evolution of coordination number versus effective vertical stress for all samples converge to a unique curve, which may depict the minimum value of coordination number for the load-bearing structure to sustain the effective stress. Different anisotropic sources undertake different roles in shear resistance. The contribution of tangential contact force anisotropy to shear resistance is gradually replaced by contact normal anisotropy.

Numerical exploration of the behavior of coal-fouled ballast subjected to direct shear test

Ballast undergoes gradual and irreversible fouling process during its service life. To explore the influence of fouling materials on the mechanical properties of ballast aggregates, a series of large-scale direct shear tests were carried out on coal-fouled ballast. Laboratory results show that increasing fouling fines decreases both the shear strength and the volume dilation of ballast aggregate. The corresponding DEM numerical models were established, with the help of which some microscopic characteristics, including the coordination number, the contact force, the force anisotropy and the rotation of ballast particles, were investigated. Using the calibrated DEM model, the size gradation effect of fouling fines on the mechanical behavior of ballast aggregates were explored. The results show that fouled ballast aggregates exhibit lower shear stresses, volume dilations, peaking shearing resistance angles and dilation angles than clean ballast, since they generate smaller coordination numbers, average contact forces, force anisotropies and particle rotations as observed by numerical simulations.

Effect of particle type on the shear behaviour of granular materials

In discrete element method (DEM) simulations, multi-sphere (MS) clumped and convex particles are two main particle models that are used to study the mechanical behaviours of granular materials. Of interest is the evaluation of the effect of multiple contacts between clumped particles or single contacts between convex particles on the mechanical behaviours of granular materials. In this context, a series of drained triaxial compression tests were conducted on convex true (CT) ellipsoids and MS ellipsoids with aspect ratios (ARs) ranging from 1.0–2.0. The microscale results indicate that at a given AR, the critical friction angle φc changes with the particle type, whereas the peak friction angle φp is nearly independent of the particle type. The anisotropic analysis provides underlying mechanisms of the shear strength evolution from two perspectives. First, the anisotropies of granular materials are essential to shear strength as the deviatoric (q)-to-effective mean (p′) stress ratio can be expressed as the sum of the anisotropies, i.e., q/p′ ≈ 0.4ac+ 0.4an + 0.6at, where ac, an and at are the normal contact anisotropy, normal contact force anisotropy and tangential contact force anisotropy, respectively. For all samples, ac and an underpin the shear strength and are influenced by the particle type. The similar φp displayed by the CT and MS ellipsoids does not translate to similar an and ac but similar ac+an for the two particle types. In addition, owing to their larger ac+an, the CT ellipsoids have a higher φc than the MS ellipsoids. Second, there is a satisfactory linear relationship between q/p′ and ac within strong and non-sliding (sn) contacts acsn (i.e., q/p′ = kacsn), where k is the fitting parameter. Accordingly, in the peak state, the subtle difference in shear strength is attributed to the greater acsn in the CT ellipsoids than in the MS ellipsoids that is counteracted by the smaller k. However, in the critical state, the greater difference in acsn between the CT and MS ellipsoids is partially offset by the smaller difference in k, causing a higher φc in the CT ellipsoids than in the MS ellipsoids.

On the role of pre-existing discontinuities on the micromechanical behavior of confined rock samples: a numerical study

The deformation process and failure mechanism of rock mass with increased density of initial joints subjected to confined stress state are investigated in this study using discrete element method (DEM). A numerical model of standard size granite samples is developed and validated using experimental data for both intact and jointed rocks. The micro-parameters of the rock material are first determined, and the effects of the rock discontinuity on strength, deformability, stress–strain relationship, and failure modes are then investigated at the macro-scale level. Analyses are also performed to examine the tensile and shear crack distributions, fragmentation characteristics, particle kinematics, and energy dissipation to advance the current understanding of the deformation processes and failure mechanisms of jointed rock masses. The microscopic evolutions in the fabric and force anisotropy during loading and distributions of contact forces provide insights into the influence of increasing initial jointing on the macroscopic deformational behavior of the rock. The results show how the deceleration in the growth of fabric and contact force anisotropies develops and confirms that the increase in initial jointing and the associated changes in microstructure can restrain the development of anisotropy, thereby reducing significantly the strength of the rock samples.

CFD-DEM model to assess stress-induced anisotropy in undrained granular material

This paper presents CFD-DEM simulations of undrained true triaxial tests on a granular soil. A CFDEM solver that considers compressible fluid and moving meshes has been developed and calibrated against the results of laboratory testing on Nevada sand. The effect of the intermediate stress ratio (b) on the macro- and micro-mechanical features of undrained granular assemblies was studied. The tests were repeated at different confining pressures, and the trends were similar to each other. The lowest effective frictional resistance was observed for specimens for which b = 0 and the highest value was obtained for specimens with b = 0.5. An increase in b caused samples to exhibit the greatest dilative behavior and increased the absolute maximum negative excess pore pressure. The stress-force-fabric equation that represents the stress state of the assembly in terms of the fabric anisotropy and contact force anisotropy tensors was used to study the micromechanics of the undrained granular samples. The tests were varied from compression to extension in order to qualitatively and quantitatively analyze the evolution of anisotropy under anisotropic loading conditions. Observations on the microstructural evolution of undrained samples were in agreement with those already reported for drained samples.

A numerical study of particle friction and initial state effects on the liquefaction of granular assemblies

Liquefaction of sandy soil due to cyclic loading can result in catastrophic damage to the built environment. Liquefaction has been previously studied through field testing, laboratory experiments, and numerical simulations. However, the particle-scale behavior of granular materials during the initiation of liquefaction has not been comprehensively quantified. In the current work, the discrete element method is employed to study the effect of global void ratio, initial confining stress, overconsolidation ratio, and particle friction on liquefaction resistance. Mechanical coordination number, local void ratio distribution (LVRD) entropy, fabric anisotropy and average rotational velocity are quantified in each assembly to provide insight into the particle-scale physics governing liquefaction resistance. Results show that lower global void ratio, increased confining stress, higher OCR values, and higher particle friction all increase liquefaction resistance. Immediately prior to the onset of liquefaction, the mechanical coordination number in each assembly sharply decreased to approximately 2.5, with the remaining contacts attributed primarily to particle collision after liquefaction initiation and fabric collapse. Anisotropy induced in the cyclic loading process was due to normal contact force anisotropy, which was more prominent in the specimens with higher initial confining pressures. Liquefaction resistance for overconsolidated specimens was found to be lower than that of normally consolidated specimens at the same void ratio. We observe liquefaction resistance to be sensitive to the coefficient of interparticle sliding friction, especially for lower friction coefficients. Average particle rotational velocities are shown to increase with increasing interparticle friction. The quantity of energy dissipated through frictional sliding was controlled by both the rate of dissipation and the number of loading cycles to liquefaction. In sum, the simulations elucidate significant connections between micromechanical properties and liquefaction response at different initial states and with different particle frictions.

New insights into the effect of interparticle friction on the critical state friction angle of granular materials

This letter examines the effect of interparticle friction (μ) on the critical state friction angle (φcs) of granular materials via the discrete element method. A series of drained triaxial tests are conducted on multisphere ellipsoids. The results indicate that φcs first increases with μ and then reaches a plateau when μ ≥ 0.3. Anisotropic analysis provides new insights into the underlying mechanisms of the φcs evolution from two perspectives. First, the initial increase of φcs results from the increases of contact normal anisotropy ac, normal contact force anisotropy an and tangential contact force anisotropy at; subsequently, the saturation of φcs is a consequence of the decrease of an being compensated by the increase of at. Second, the relationship between the stress ratio q/p and the contact normal anisotropy within the strong and nonsliding contacts acsn is nearly linear for ellipsoids (i.e., q/p = kacsn). Accordingly, the initial increase of φcs is related to the increase of k and acsn at low μ. The plateau of φcs at high μ can be attributed to the decrease of acsn being compensated by the increase of k.

Shear behaviors of granular mixtures of gravel-shaped coarse and spherical fine particles investigated via discrete element method

The shear behaviors of granular mixtures are studied using the discrete element method. These granular materials contain real gravel-shaped coarse particles and spherical fine particles. Dense samples have been created by the isotropic compression method. The samples are then sheared under drained triaxial compression to a large strain to determine the peak and residual shear strengths. The emphasis of this study is placed on assessing the evolutions of contributions of the coarse-coarse (CC) contacts, coarse-fine (CF) contacts and fine-fine (FF) contacts to the peak and critical deviator stresses. The results are used to classify the structure of granular mixtures. Specifically, the granular mixtures are fine-dominated or coarse-dominated materials when the coarse particle content is <30%–40% or >65%–70%, respectively. A comparison with previous findings suggests that the spherical binary mixtures will become coarse-dominated materials at a relatively larger coarse particle content (i.e., 75%–80%) than this study (i.e., 65%–70%), which is attributed to the particle shape effect of coarse particles. A microscopic analysis of CC, CF and FF contacts at the peak and critical states, including normal contact forces and proportions of strong and weak contacts of each contact type to total contacts, reveals why the contributions of CC, CF and FF contacts to the peak and residual shear strengths are varied. Finally, a detailed analysis of the anisotropies indicates that the increases of peak and residual shear strengths are primarily related to the gradual increases in geometrical anisotropy ac and tangential contact force anisotropy at to compensate for the continuous decrease in normal contact force anisotropy an. Furthermore, it is interesting to note that the branch vector frame provides a better linear relationship between the stress ratio and the geometric anisotropy of the strong and nonsliding subnetwork than the contact frame for the coarse-dominated materials.

Influence of stress anisotropy on stress distributions in gap-graded soils

The behaviour of gap graded soils comprising non-plastic fines (sand or silt) mixed with a coarser sand or gravel fraction has received attention from researchers interested in internal instability under seepage loading (a form of internal erosion) as well as researchers interested in load:deformation responses. Skempton and Brogan [1] postulated that resistance to seepage induced instability depends upon the proportion of the overall applied stress that is transmitted by the finer fraction. Shire et al. [2] explored Skempton and Brogan’s hypothesis using DEM simulations to look at the proportion of the applied stress transmitted by the finer fractions (α) in ideal isotropic samples. They showed that at low fines contents (FC&lt; FC*) the average stress transmitted by the finer grains is less than the applied stress (α&lt;1), while for FC&gt;FC+ the fines play a key role in stress transmission (α&gt;1); for FC*&lt;FC&lt; FC+, α depends on the sample density. The current contribution describes a series of constant p’ DEM triaxial test simulations carried out to assess the evolution of stress heterogeneity with shearing. The simulation data generated indicate that a sample can transition from being fines dominated (with the fines transmitting a significant proportion of the applied stress and α ≥1) to coarse or sand- dominated (with α &lt;1) as the material dilates during shear deformation. While α reduces as the samples dilate, the relationship between the α and the sample void ratio is non-trivial. The anisotropy of the coarse-coarse contact network exceeds the overall contact force anisotropy; this indicates that the deviator stress is transmitted through a strong force network passing through the coarse-coarse contacts supported by the fine-coarse contacts.

Rheology of granular materials composed of crushable particles.

We investigate sheared granular materials composed of crushable particles by means of contact dynamics simulations and the bonded-cell model for particle breakage. Each particle is paved by irregular cells interacting via cohesive forces. In each simulation, the ratio of the internal cohesion of particles to the confining pressure, the relative cohesion, is kept constant and the packing is subjected to biaxial shearing. The particles can break into two or more fragments when the internal cohesive forces are overcome by the action of compressive force chains between particles. The particle size distribution evolves during shear as the particles continue to break. We find that the breakage process is highly inhomogeneous both in the fragment sizes and their locations inside the packing. In particular, a number of large particles never break whereas a large number of particles are fully shattered. As a result, the packing keeps the memory of its initial particle size distribution, whereas a power-law distribution is observed for particles of intermediate size due to consecutive fragmentation events whereby the memory of the initial state is lost. Due to growing polydispersity, dense shear bands are formed inside the packings and the usual dilatant behavior is reduced or cancelled. Hence, the stress-strain curve no longer passes through a peak stress, and a progressive monotonic evolution towards a pseudo-steady state is observed instead. We find that the crushing rate is controlled by the confining pressure. We also show that the shear strength of the packing is well expressed in terms of contact anisotropies and force anisotropies. The force anisotropy increases while the contact orientation anisotropy declines for increasing internal cohesion of the particles. These two effects compensate each other so that the shear strength is nearly independent of the internal cohesion of particles.