Mechanical Behavior Of Granular Materials Research Articles

An extended in-situ method to improve the understanding of fracture mechanics of granular materials using sound measurements

In this work we present a new experimental technique alternative to Acoustic Emissions, which makes use of sound signal sensing, to complement the assessment of the mechanical behaviour of sand grains. A post-processing protocol is also proposed. By using this technique in combination with microscopy during in-situ compression tests, it was possible to capture complementary features in the complex mechanical behaviour of granular materials. In addition to that, dominant acoustic frequencies in the sound emitted by sand grains during failure were captured. The method has been applied to study the effects of chemical composition, morphology and grain sizes on the failure mechanics of three types of single sand grains. The advantages of this approach over other traditional techniques to capture failure events during cracking of granular materials have also been clearly demonstrated.

Simulations of large-scale triaxial shear tests on ballast aggregates using sensing mechanism and real-time (SMART) computing

Since Discrete Element Method (DEM) was first introduced for modeling micromechanical interactions of granular materials back in late 1970s, significant progress has been made to improve the performance of DEM algorithms. For example, a variety of approaches have been developed to simulate triaxial tests using DEM to better understand the fundamental mechanical behavior of granular materials. Nevertheless, potential error accumulation over the necessary large number of timesteps as a part of the explicit time integration may undermine the simulation accuracy. This paper presents the development, implementation and validation of a computing scheme that is based on real-time data fusion between a sensing mechanism and real time (SMART) computing. This computing framework consists of: (1) real-time data acquisition of particle kinematics through a wireless instrumentation called “SmartRocks” that are embedded at discrete locations in a granular assembly, and (2) a built-in data-fusion-based algorithm using the Kalman filter to integrate the prediction generated by DEM and the measurements reported by “SmartRocks.” To evaluate the performance of the SMART computing algorithm, laboratory large-scale triaxial tests on ballast specimens were conducted and the results were compared to traditional DEM-only and SMART computing simulations. It is concluded the SMART computing improved the simulation accuracy over the DEM-only simulations in terms of the deviatoric stress vs. axial strain, volumetric strain vs. axial strain, and final deformed specimen shape, and hence can be used to model large-scale triaxial tests with high fidelity.

On the breakage function for constructing the fragment replacement modes

The fragment replacement method (FRM), a particle breakage simulation method, is often used in discrete element simulations to investigate the particle breakage effect on the mechanical behavior of granular materials. The fragment size distribution of the fragment replacement mode of FRM, which is generally generated based on the fragmentation characteristics of single particles after uniaxial compression, affects the breakage process and the mechanical behavior of the particle assembly. However, existing fragment replacement modes are seldom generated based on experimental data analysis. To capture the fragmentation process and investigate the breakage function for the construction of the fragment replacement mode, 60 numerical single particle compression tests were implemented by DEM. The bonded-particle model was applied to generate the crushable rock particles. The numerical simulations were qualitatively validated by experimental results, and the fragment size of broken single particles was analyzed. The fractal dimension was used to describe the fragmentation degree of single particles after compression. The fragmentation degree was random, and the fractal dimensions of the 60 tests at the same loading displacement fit the Weibull distribution well. The characteristic fractal dimension increased with increasing loading displacement, indicating that the fragmentation of single particles is a gradual process. According to the overall breakage function of the 60 tests at the first bulk breakage, a two-stage distribution model with 4 parameters was proposed and validated by the numerical and experimental results. The various fracture patterns of a single particle at the first bulk breakage under compression tests were well captured by the two-stage distribution model. Finally, an initial application strategy using the two-stage distribution model to construct fragment replacement modes was discussed and presented.

Discrete element modeling of first shear strain gradient effects on mechanical behaviors in granular materials

The effects of strain gradient on the mechanical behavior of granular materials have attracted attention from many researchers. In this paper, the effects of the first shear strain gradient in granular materials are focused on. Granular assemblies with various particle radii and porosities are built through a two-dimensional discrete element method (2D-DEM) simulations. The results indicate that the macro shear stress is insensitive to the first shear strain gradient at low strains, but is indeed affected at high strains; the third order stress conjugated with the first shear strain gradient is sensitive to the first shear strain gradient in all deformation cases; the third order work done by the third order stress and the ratio of it versus the total work are affected by the first shear strain gradient; the evolutions of the invariants of the third order stresses present severe change of the local relative vertical displacement of particles, which lead to localization occurrence. Based on DEM simulations, it is found that only the effect consideration of the first shear strain gradient on the macro shear stress is not sufficient, whereas the effect on work should also be taken into account and the third order work as a part of strain energy cannot be ignored, which is falsely classified as a portion of the accumulated energy dissipated by frictional sliding.

Triaxial behavior of granular material under complex loading path by a new numerical true triaxial engine

A new numerical true triaxial engine based on discrete element method accounting for rolling resistance contact is developed. By this engine, we have simulated mechanical behavior of granular materials under complex stress loading path in this study. Stress-strain responses of a kind of typical granular sand under several stress loading path in meridian and deviatoric stress space are provided. The results show that the three dimensional effects like the intermediate principal stress play an important role in the modeling processes. Theoretical analysis in strength characteristic implies the strength criteria with three parameters such as unified strength criterion and van Eekelen strength criterion are capable of describing cohesionless granular material behaviors in three dimensional stress states. Moreover, the case study for Chende sand further demonstrates the numerical true triaxial engine, is a potential tool. As compared to conventional triaxial compression test, this new developed apparatus could be widely used to “measure” elastic-plastic behavior in three dimensional stress space for finite element analysis in geotechnical problems.

Effect of Particle Breakage and Shape on the Mechanical Behaviors of Granular Materials

The particle breakage property under loading is an important factor affecting the nonlinearity of the shear strength and stress‐strain curves of coarse‐grained soils. The macromechanical behaviors of coarse granular materials under consolidation and drainage shearing were tested by using a large true triaxial apparatus. The particle breakage mechanism has been analyzed by the fluctuation change of stress‐strain curve and particle composition change. It was shown that the particle shape is an extremely important microproperty of the influence of granular material breakage. The variation rules of the internal friction angle and interlocking strength with the index of fine‐grained breakage were sorted out, and the critical particle size for measuring the two friction modes under the given gradation was determined to be 1 mm. In addition, the numerical analysis was conducted by simulating the microshape parameters of particles. The conclusion is as follows: (1) The effect of shape parameters on shear strength can be simulated using the smoothness index Fd. (2) Compared with spherical particles, irregular‐shaped particles lead to a decrease in the number of strong force chains. Moreover, more coordination numbers are needed to maintain a stable configuration, and the shear strength is improved.

DEM simulation of shear vibrational fluidization of granular material

Fluidization of dry granular material is the transition from a solid state to a liquid state when sufficient energy is applied during vibration. This behavior is important because it is closely related to deformations of geotechnical structures during an earthquake. The scientific challenge lies in the understanding on how strain localization is related to the fluidization zone during the entire shearing process. Despite the importance of the mechanical behavior of granular material during fluidization, it cannot be easily characterized using traditional direct shear test. In this paper, 2D DEM model is firstly conduct, shear vibrational fluidization is defined for dry granular material, and the discrete element method has been used to simulate the direct shear test on granular material under vibrational loading during shearing. The peak, residual and vibro-residual shear strength envelopes have been obtained from the numerical simulations. Three distinct zones have been identified in the upper shear box based on the observed changes in volumetric strain before vibration. During vibration, fluidization occurs in the three zones with the characteristics that the shear stress, porosity, volumetric strain, and the coordination number drop to relatively lower values. During vibration, material becomes denser than the critical state, and strain localization has been relieved. Densification of the material at the shear zone leads to a strengthening of the material which increases the shearing resistance after vibration. Furthermore, a comparison of the 2D and 3D simulations is performed. Results reveal that the motion of particles in the out-of-plane direction in the 3D simulations lead to smoother shear stress and more consistent with the experimental result.

Rattlers' contribution to granular plasticity and mechanical stability

The mechanical behavior of granular materials is widely governed by microstructure reorganizations. This constant evolution of the microscale geometry is often taken into account directly at the macroscale within the plasticity context, and more particularly non-associated plasticity. In this paper we propose to revisit the non-associated plastic behavior of granular materials with respect to material instability assessment in terms of the loss of positiveness of the second-order work. It is shown that large incremental plastic strain is a necessary condition for the existence of mechanical instability. The ability of a material to develop substantial plastic incremental strain is then related to the existence of rattlers, i.e., free particles that get jammed into force chains when existing contact networks fail to adapt to incremental loadings. This link between rattlers, plastic deformation and the vanishing of the second-order work is explicitly derived i) from the micro-formulation of the second-order work and ii) directly from discrete element simulations.

Fractal dimension of roughness: Influence of grain size and granular class

The soil structure can be described as an assembly of elements of various sizes separated by a complex system of cracks and fractures, since the grains of the soil are differentiated by their shape, size and orientation. They are thus differently associated and related, their masses can form complex and irregular configurations which are in general extremely difficult to characterize in exact geometric terms. To understand the mechanical behavior of granular materials, it is then necessary to characterize the grains using the fractal dimension which is a characteristic that indicates the degree of irregularity and fragmentation of the latter.
 This experimental work consists in studying the influence of the parameters variation: granular class, grain size and normal stress applied during Casagrande's direct shear tests on the roughness fractal dimension calculated with the method of Box counting. The analysis of the results obtained at the end of a granulometric variation which caused a variation of the fractal dimension of grain roughness. This variation made it possible to analyze the level of fragmentation suffered by the sandstone grains during the various shear tests. This fragmentation produces fines that are the source of variations in the mechanical properties of the sandstone material.

Sensing Mechanism and Real-Time Computing for Granular Materials

AbstractThe discrete element method (DEM) has been widely used to study the mechanical behavior of granular materials. However, potential error accumulation over the required large number of time s...

Evaluation of granular particle roundness using digital image processing and computational geometry

The engineering behaviors of granular materials has been proven to be influenced by particle roundness. Based on several computational geometry algorithms and a well-acknowledged roundness definition, an innovative roundness evaluation method is developed. Algorithm verifications are performed to verify the reliability and the capacity of this proposed method. Relative to the traditional chart method, the proposed method is more effective and more objective. The motivation of this study is to facilitate future studies on the relationship between microscopic particle shape and the microscopic mechanical behavior of granular materials.

The influence of rolling resistance on the stress-dilatancy and fabric anisotropy of granular materials

The effects of rolling resistance on the stress-dilatancy behavior and fabric anisotropy of granular materials were investigated through a three-dimensional discrete element method (DEM). A rolling resistance model was incorporated into the DEM code PFC3D and triaxial DEM simulations under simulated drained and undrained conditions were carried out. The results show that there existed a threshold value of the rolling friction. When the rolling friction was smaller than this value, the mechanical behavior of granular materials under both drained and undrained conditions were substantially influenced by the rolling friction, but the influence diminished when it was larger than the threshold value. A linear relationship has been observed between the dilatancy coefficient and the natural logarithm of the rolling-friction coefficient when it was smaller than the threshold value. An increase in the rolling friction led to an increase in the fabric anisotropy of all strong contacts under both testing conditions until the threshold value was attained. The investigation on the effect of rolling friction on the microstructure of granular materials revealed that the rolling friction enhanced the stability of force chains, which resulted in the difference in the stress-dilatancy behavior. Finally, the relationship between the stress ratio q/p $$^{\prime }$$ and the fabric measure at strong contacts $$\hbox {H}_{\mathrm{d}}^{\mathrm{s}} /\hbox {H}_{\mathrm{m}}^{\mathrm{s}}$$ was found independent of the inter-particle friction, rolling friction and testing conditions.

Multi-periodic boundary conditions and the Contact Dynamics method

For investigating the mechanical behavior of granular materials by means of the discrete element approach, it is desirable to be able to simulate representative volume elements with macroscopically homogeneous deformations. This can be achieved by means of fully periodic boundary conditions such that stresses or displacements can be applied in all space directions. We present a general framework for periodic boundary conditions in granular materials and its implementation more specifically in the Contact Dynamics method.

In situ grain fracture mechanics during uniaxial compaction of granular solids

Grain fracture and crushing are known to influence the macroscopic mechanical behavior of granular materials and be influenced by factors such as grain composition, morphology, and microstructure. In this paper, we investigate grain fracture and crushing by combining synchrotron x-ray computed tomography and three-dimensional x-ray diffraction to study two granular samples undergoing uniaxial compaction. Our measurements provide details of grain kinematics, contacts, average intra-granular stresses, inter-particle forces, and intra-grain crystal and fracture plane orientations. Our analyses elucidate the complex nature of fracture and crushing, showing that: (1) the average stress states of grains prior to fracture vary widely in their relation to global and local trends; (2) fractured grains experience inter-particle forces and stored energies that are statistically higher than intact grains prior to fracture; (3) fracture plane orientations are primarily controlled by average intra-granular stress and contact fabric rather than the orientation of the crystal lattice; (4) the creation of new surfaces during fracture accounts for a very small portion of the energy dissipated during compaction; (5) mixing brittle and ductile grain materials alters the grain-scale fracture response. The results highlight an application of combined x-ray measurements for non-destructive in situ analysis of granular solids and provide details about grain fracture that have important implications for theory and modeling.

Effect of Anisotropy on the Resilient Behaviour of a Granular Material in Low Traffic Pavement.

Granular materials are often used in pavement structures. The influence of anisotropy on the mechanical behaviour of granular materials is very important. The coupled effects of water content and fine content usually lead to more complex anisotropic behaviour. With a repeated load triaxial test (RLTT), it is possible to measure the anisotropic deformation behaviour of granular materials. This article initially presents an experimental study of the resilient repeated load response of a compacted clayey natural sand with three fine contents and different water contents. Based on anisotropic behaviour, the non-linear resilient model (Boyce model) is improved by the radial anisotropy coefficient γ3 instead of the axial anisotropy coefficient γ1. The results from both approaches (γ1 and γ3) are compared with the measured volumetric and deviatoric responses. These results confirm the capacity of the improved model to capture the general trend of the experiments. Finally, finite element calculations are performed with CAST3M in order to validate the improvement of the modified Boyce model (from γ1 to γ3). The modelling results indicate that the modified Boyce model with γ3 is more widely available in different water contents and different fine contents for this granular material. Besides, based on the results, the coupled effects of water content and fine content on the deflection of the structures can also be observed.

A novel experimental device for investigating the multiscale behavior of granular materials under shear

In this paper, we report a set of experiments performed on a novel mechanical device that allows a specimen composed of a two-dimensional opaque granular assembly to be subjected to quasi-static shear conditions. A complete description of the grain-scale quantities that control the mechanical behavior of granular materials is extracted throughout the shear deformation. Geometrical arrangement, or fabric, is quantified by means of image processing, grain kinematics are obtained using Digital Image Correlation and contact forces are inferred using the Granular Element Method. Aiming to bridge the micro-macro divide, macroscopic average stresses for the granular assembly are calculated based on grain-scale fabric parameters and contact forces. The experimental procedure is detailed and validated using a simple uniaxial compression test. Macroscopic results of shear stress and volumetric strain exhibit typical features of the shear response of dense granular materials and indicate that critical state is achieved at large deformations. At the grain scale, attention is given to the evolution of fabric and contact forces as the granular assembly is sheared. The results show that shear deformation induces geometrical (fabric) and mechanical (force) anisotropy and that principal stresses and force orientation rotate simultaneously. At critical state, stress, force and fabric orientation reach the same value. By seamlessly connecting grain-scale information to continuum scale experiments, we shed light into the multiscale mechanical behavior of granular assemblies under shear loading.

Gyratory abrasion with 2D image analysis test method for evaluation of mechanical degradation and changes in morphology and shear strength of compacted granular materials

Mechanical degradation of granular materials can significantly influence the performance and durability of pavement systems. The commonly used Los Angeles (LA) abrasion test does not test the entire gradation of the material, nor simulate the compaction and field loading conditions. A new Gyratory Abrasion and Image Analysis (GAIA) test method was developed in this study and compared with the LA abrasion test for five granular material types. Results show that the GAIA test can address shortcomings of the conventional test, provide insight into mechanical behavior of granular materials during compaction, and enable performance-based specifications for field compaction of granular materials.

The influence of particle geometry and the intermediate stress ratio on the shear behavior of granular materials

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 $$(b=({\upsigma }_{2}'-{\upsigma }_{3}')/({\upsigma }_{1}'-{\upsigma }_{3}'))$$ affect the macro- and 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.

Discrete numerical modeling of granular materials considering crushability

The aim of this study is to numerically investigate the influence of particle breakage on the mechanical behavior of granular materials using a discrete element method (DEM). To enable particle crushing, non-crushable elementary particles are boned together to represents the granular aggregates which can be crushed when the external force exceeds its strength. The flaw of the aggregate was also modeled by randomly distributed void. Single particle crushing tests were carried out to determine the distribution of particle strength. The results of single particle crushing tests illustrate that the simulated single particle fracture strength and pattern agree well with the Weibull’s distribution equation. Conventional oedometer tests, drained monotonic and cyclic triaxial tests were also carried out to investigate the crushing of the aggregates and the associated mechanical behaviors. The effect of confining pressure on the crushing of aggregates and the mechanical behavior was also analyzed. It was found that the peak stress and dilation decrease significantly when particle crushing was considered. The deformation behavior of the specimen is essentially controlled by two factors: particle rearrangement - induced dilation and particle crushing - induced contraction. The increase of permanent strain and the reduction of dilation were observed during cyclic loading and they tend to reach a stable state after a certain number of cycles. The crushing of aggregate is most significant in the first two cycles. The results also indicated that for the same axial strain the volumetric strain and the bound breakage in the cyclic loading tests are significantly larger than that in the monotonic loading tests, especially at high cyclic stress ratio.

Three-dimensional DEM investigation of critical state and dilatancy behaviors of granular materials

The critical state is significant to the mechanical behaviors of granular materials and the foundation of the constitutive relations. Using the discrete element method (DEM), the mechanical behaviors of granular materials can be investigated on both the macroscopic and microscopic levels. A series of DEM simulations under true triaxial conditions have been performed to explore the critical state and dilatancy behavior of granular materials, which show the qualitatively similar macroscopic responses as the experimental results. The critical void ratio and stress ratio under different stress paths are presented. A unique critical state line (CSL) is shown to indicate that the intermediate principal stress ratio does not influence the CSL. Within the framework of the unique critical state, the stress–dilatancy relation of DEM simulations is found to fulfill the state-dependent dilatancy equations. As a microscopic parameter to evaluate the static determinacy of the granular system, the redundancy ratio is defined and investigated. The results show that the critical state is very close to the statically determinate state. Other particle-level indexes, including the distribution of the contact forces and the anisotropies, are carefully investigated to analyze the microstructural evolution and the underlying mechanism. The microscopic analysis shows that both the contact orientations and contact forces influence the mechanical behaviors of granular materials.