Properties Of Granular Materials Research Articles

Fracture process zone in crystalline rock: effect of specimen size and shape

Ability to predict fracture properties of granular materials based on their size and loading conditions needs rigorous experimental evidence. Charcoal granite specimens of various sizes and geometries are tested under three- and four-point bending to investigate the effect on the fracture toughness of rock and size of the fracture process zone calculated using Digital Image Correlation (DIC), with validation provided by Acoustic Emission (AE). Two different methods to evaluate the length of the fracture process zone using DIC are adopted: the first one assumes that a traction free crack does not propagate in the pre-peak regime, while the second one hypothesizes that a cohesionless crack may exist at peak load before unstable crack growth. The effects of specimen size, geometry, and loading conditions are found to be more prominent for the specimen sizes used in the laboratory but are predicted to become less significant and eventually negligible as the specimen size increases. DIC results are in general agreement with localization of AE events, but the former technique is suggested due to greater resolution and ability of continuous measurements of the fracture process zone dimensions.

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.

The Effect of a Moving Boundary on the Shear Strength of Granular Materials in a Direct Shear Test

The boundary state significantly influences the soil shear strength. Therefore, it is necessary to overcome the limitations of existing indoor test instruments and determine the differences in the shear properties of granular materials to ensure the economic feasibility and mechanical integrity of engineering structures. In this study, the core formula for the direct shear test was derived from the static balancing analysis of the shear box, the external force on the specimen, and the internal force on the shear surface. Three loading methods were then developed by the staggered state of the upper and lower boxes: the upper box moving shear loading method (UM), the lower box moving shear loading method (LM), and the bidirectional moving shear loading method (BM). Finally, by manipulating the motion boundary, the discrete element method (DEM) was employed to simulate the shear test of granular materials. Among the three loading methods, the order of the peak shear stresses was as follows: UM > BM > LM. Moreover, the order of the sample post-peak stress uniformities was as follows: LM > BM > UM. A shear strength conversion formula was then proposed. The findings of this study promote the advancement of the shear mechanics theory of granular materials in direct shear testing and can serve as a scientific basis for the design and manufacture of shear equipment.

Multi-GPUs DEM algorithm and its application in the simulation of granular materials

The Discrete Element Method (DEM) is one of the most common numerical approach for modeling the physical and mechanical properties of granular materials. However, its computational efficiency can be a major bottleneck, which significantly hinders its application in engineering fields. To overcome this challenge, a multi-GPU framework with OpenMP has been developed. In this framework, the DEM particles in 3D space and their corresponding contact information are sorted in a given direction in the simulation, and each GPU device handles a subdomain of particles and relative contacts. Additionally, the contact information is densely arranged to minimize memory usage. To further enhance efficiency, sorting and packing algorithms for the contact information have been introduced. During calculating loop, the number of contacts on each device is monitored, and the spatial division of devices is adjusted to balance memory distribution. The efficacy of the multi-GPU algorithm is verified through a chute flow test. Using numerical results, the segregation process and mechanics of granular materials during sliding have been studied in detail. Furthermore, the simulations demonstrate that the developed multi-GPU algorithm greatly enhances computational efficiency and reduces memory usage per device.

DEM study on mixing behaviors of concave-shaped particles in rotating drum based on level-set method

Granular mixing is a complex phenomenon that is commonly encountered in various engineering disciplines. A large number of past studies have mainly focused on the mixing properties of convex-shaped granular materials, while the mixing behaviors of concave-shaped granular materials have not been well studied. In this study, spherical harmonic functions are used to describe the spherical and concave shapes of individual particles. The level set function is an implicit function consisting of a set of points that can be used to determine the contact points between particles. Then, the influences of the particle shape and rotational speed on the mixing behaviors of the granular material within a horizontal drum are analyzed by the discrete element method (DEM). Results indicate that concave particles have higher coordination numbers and closer contact patterns than spherical particles, which results in greater normal collision forces, larger dynamic angle of repose and lower mixability.

Thermodynamic constitutive model for granular soils considering particle shape distribution

Particle shape has a significant effect on the shear strength and shear dilatancy properties of granular materials. This study presents a granular thermodynamic theory investigate the effects of particle shape and distribution on the mechanical properties and behavior of granular materials. The theory model outcomes closely resemble experimental results, effectively capturing the impact of particle shape on the mechanical properties and shear dilation of granular materials. The paper analyzes the relationship between a granular system's plastic behavior and granular temperature and explores the influence of irregularly shaped granular on the system's strength and kinetic energy activity. The granular temperature behavior during external loading is studied, showing that granular temperatures increase to a maximum value before gradually decreasing to a more stable state. Simulation results based on the proposed model also indicate obvious effects of nonuniform particle-shape distribution on the mechanical properties of granular materials, providing a comprehensive insight into the underlying mechanisms of the particle-shape effects from the perspective of thermodynamics.

A physically consistent Discrete Element Method for arbitrary shapes using Volume-interacting Level Sets

The properties of granular materials depend strongly on the shapes of their individual constituent particles or granules. Nonetheless, incorporating the effects of non-spherical or complex particle shapes into existing modelling frameworks, such as the discrete element method (DEM), has remained challenging. In this work, we propose the volume-interaction level set DEM (VLS-DEM) approach for carrying out physically accurate simulations of particles with arbitrary geometries. VLS-DEM builds upon level set DEM (LS-DEM), both of which implicitly define the geometry of a particle through a discrete signed distance function. However, instead of using surface nodes to compute the interparticle forces, VLS-DEM uses the overlap volume as computed by an Octree integration algorithm. This addresses some of the shortcomings of LS-DEM in terms of the accuracy and precision of the shape description and opens up the possibility for bottom-up parametrisation methods. A number of tests were performed to compare VLS-DEM with regular DEM, LS-DEM, and analytical models. VLS-DEM is shown to give physically accurate results, comparable to analytical theory, even for highly complex systems such as those with concave interlocked particles.

Sound characteristics of disordered granular disks: effects of contact damping

We investigate numerically the sound properties of disordered dense granular packings in two dimensions. Employing linear equations of motion and excluding contact changes from our simulations, we demonstrate time evolution of sinusoidal standing waves of granular disks. We varied the strength of normal and tangential viscous forces between the disks in contact to explore the dependence of sound characteristics such as dispersion relations, attenuation coefficients, and sound speeds on the contact damping. For small wave numbers, the dispersion relations and sound speeds of acoustic modes are quite insensitive to the damping. However, a small dip in the phase speed of the transverse mode decreases as the viscous force in normal direction increases. In addition, the dispersion relation of the rotational mode differs qualitatively from the theoretical prediction for granular crystals. Therefore, disordered configurations with energy dissipation play a prominent role in sound properties of granular materials. Furthermore, we report how attenuation coefficients depend on the contact damping and quantify how they differ from the prediction of lattice theory. These improved relations, based on our numerical results, can in future be compared to advanced theories and experiments.

New multifunctional bromine-active polymers: synthesis, properties, and antimicrobial activity

The increase in the frequency and scale of epidemics of infectious diseases gives extreme urgency to the development of new technologies for antiseptic and disinfectant treatment of various media, as well as materials/reagents for their implementation. Antimicrobial polymer materials of various chemical structures, including those containing halogen-active functional groups, are promising in this regard. This work is devoted to the synthesis and investigation of the properties of granular and fibrous polymer materials with immobilized N-bromosulfonamide groups of different structure. It is shown that copolymers of styrene with divinylbenzene and polypropylene can be used as a carrier polymer. A technique has been developed that allows obtaining polymers with a content of up to 23 % of immobilized active bromine. The compliance of the synthesized materials with the declared structure has been proven by IR spectroscopy and a complex of chemical methods. A decrease in the strength of the obtained polymers compared to the original carriers has been observed, especially in the case of fibers. The stability of the synthesized polymers during storage is lower that of the previously described chlorine-active analogs. For the quantitative determination of active bromine in the target materials, a technique based on its rapid diffusion from the polymer into the taurine solution has been developed. Microbiological research has shown that the synthesized polymers have a pronounced antimicrobial activity, which is higher than that of immobilized N-chlorosulfonamides and is manifested even in the presence of a significant organic load. The set of investigated characteristics of synthesized polymers with immobilized N-bromosulfonamide groups suggests the prospect of their use as components of antiseptic dressing materials, antimicrobial filters, devices for obtaining antiseptic solutions, and other medical products

A novel computational model and OpenFOAM solver for simulating thermal energy storages based on granular phase change materials: Advantages and applicability

In this paper, we consider hydrodynamic and heat transfer processes in thermal energy storages based on granular or encapsulated phase change materials. Such heat storages can be applied in renewable and conventional energy, safety systems, civil building, and so on. A computational model, which is based on the assumption of interpenetrating interacting continua, has been developed to simulate the processes of phase transitions, heat transfer and fluid flow in the packed bed latent heat storages. To implement this model, we chose OpenFOAM – the leading free, open source software for computational fluid dynamics and heat transfer. Solver porousHeatTransferFoam, which is based on the SIMPLE algorithm, and additional libraries have been developed in the OpenFOAM framework. The solver and the libraries allow one to model granular materials with complex enthalpy-temperature diagrams during phase transitions, thus expanding the applicability of OpenFOAM. The advantage of the solver is high computational speed – its calculation time varies from a minute to a few minutes for 1D simulations and from a few minutes to a few hours for 2D simulations depending on the mesh sizes. Comparison between numerical results obtained and known experimental data has shown that the model based on the assumption of interpenetrating interacting continua adequately describes the heat transfer processes in the packed bed latent heat storages not only for the large ratio of the storage characteristic size to the particle diameter, but also for the small one (about 7–8). In contrast to many existing computational models, which applicability is usually limited to rather narrow class of the processes, our model covers a variety of hydrodynamic and heat transfer problems in the thermal energy storages based on granular phase change materials. This computational model and OpenFOAM solver developed allow one to simulate incompressible and compressible (liquid or gaseous) flows through the packed bed latent heat storages under various boundary conditions, with isothermal and non-isothermal phase transitions, with various properties of granular materials and coolant, in wide ranges of flow velocities, operating temperatures and particle sizes.

Echoes of the hexagon: Remnants of hexagonal packing inside regular polygons

We provide evidence that for regular polygons with σ = 6 j sides (with j = 2 , 3 , …), N ( k ) = 3 k ( k + 1 ) + 1 (with k = 1 , 2 , …) congruent disks of appropriate size can be nicely packed inside these polygons in highly symmetrical configurations, which apparently have maximal density for N sufficiently small. These configurations are invariant under rotations of π / 3 and are closely related to the configurations with perfect hexagonal packing in the regular hexagon and to the configurations with curved hexagonal packing (CHP) in the circle found a long time ago by Graham and Lubachevsky [“Curved hexagonal packings of equal disks in a circle,” Discrete Comput. Geometry 18(2), 179–194 (1997)]. The packing fraction, i.e., the portion of accessible volume (area) occupied by multiple solid objects, has a role in determining the properties of granular materials and fluids. At the basis of our explorations are the algorithms that we have devised, which are very efficient in producing the CHP and more general configurations inside regular polygons. We have used these algorithms to generate a large number of CHP configurations for different regular polygons and numbers of disks; a careful study of these results has made it possible to fully characterize the general properties of the CHP configurations and to devise a deterministic algorithm that completely ensembles a given CHP configuration once an appropriate input is specified.

Time-dependent frictional properties of granular materials used in analogue modelling: implications for mimicking fault healing during reactivation and inversion

Abstract. Analogue models are often used to model long-term geological processes such as mountain building or basin inversion. Most of these models use granular materials such as sand or glass beads to simulate the brittle behaviour of the crust. In granular material, deformation is localised in shear bands, which act as an analogue to natural fault zones and detachments. Shear bands, also known as faults, are permanent anomalies in the granular package and are often reactivated during a test run. This is due to their lower strength compared to the undeformed material. When the fault movement stops, time-dependent healing immediately begins to increase the strength of the fault. Faults that have been inactive for a long time therefore have a higher strength than younger faults. This time-dependent healing, also called time consolidation, can therefore affect the structure of an analogue model as the strength of the fault changes over time. Time consolidation is a well-known mechanism in granular mechanics, but it is poorly described for analogue materials and on the timescales of typical analogue models. In this study, we estimate the healing rate of different analogue materials and evaluate the impact on the reactivation potential of analogue faults. We find that healing rates are generally less than 3 % per 10-fold increase in holding time, which is comparable to natural fault zones. We qualitatively compare the frictional properties of the materials with grain characteristics and find a weak correlation of healing rates with sphericity and friction with an average quality score. Accordingly, in models where there are predefined faults or reactivation is forced by blocks, the stability range of the fault angles that can be reactivated can decrease by up to 7∘ over the duration of 12 h. The stress required to reactivate an existing fault can double in the same time, which can favour the development of new faults. In a basin inversion scenario, normal faults cannot be inverted because of the strong misorientation, so time consolidation plays little additional role for such models.

A New Approach for Classifying the Permanent Deformation Properties of Granular Materials under Cyclic Loading

A series of medium-sized cyclic triaxial tests were performed to investigate the permanent deformation properties of granular materials. The strain rate was then plotted against loading cycles to classify the permanent deformation properties of granular materials under different cyclic stress ratios (CSRs). It was found that (1) the permanent strain rate dεp/dN was linearly correlated with loading cycles N using a double-log coordinate on the condition of CSR < 60%; (2) the deformation tendency factor β, which was extracted from the linear relationship between dεp/dN and N, significantly varied with CSR and, thus, can be adopted to identify the deformation states; (3) β > 1 implying that permanent strain accumulation ceases in limited cycles and corresponds to the plastic shakedown range, while 0 < β ≤ 1 indicates the temporary steady state, corresponding to the plastic creep range; (4) sluggish decrease or remarkable increase in dεp/dN appeared as CSR ≥ 60%, leading to soil collapsed in limited loading cycles and resulting in an incremental collapse range. The new approach was validated by the crushed tuff aggregates and subgrade materials reported previously. It is expected that the new approach will have wider applicability than the traditional one and can provide technical guidance for the design and construction of substructures in roadway and railway engineering.

Characterization of permanent deformation properties of densely-compacted unbound granular materials subjected to cyclic loading

To investigate the long-term deformation properties of unbound granular materials (UGM) that are ordinarily adopted to construct subgrade for high-speed railway, a series of medium-sized cyclic triaxial tests were performed to obtain the relationship between permanent strain and loading cycles under different cyclic stress levels. Moreover, DEM analysis was conducted for the samples to reveal the deformation mechanism and verify the strain developing tendency. It is found that the UGM samples present different long-term deformation properties under different cyclic stress levels. As cyclic stress increases, the permanent strain of UGM sample transfers from rapid stabilization to tardy stabilization, then to tardy failure and finally to rapid failure. Furthermore, the exponent in a power law function was selected as the critical indicator of deformation developing tendency. With the exponent obtained precisely in accordance with the strain rate, the deformation tendency can be analyzed quantitatively. Finally, the characteristics of interparticle force chains induced by different cyclic stress levels were obtained by DEM analysis, which provided evidences for the classification of long-term deformation properties of UGM samples. The achievements have guiding significance for the design of subgrade of both ballasted and unballasted high-speed railway.

Application and damping mechanism of particle dampers

AbstractA particle damper is a passive damping technique, which is based on the high damping properties of granular materials. The energy dissipation rate of a particle damper depends on several factors, like the type of granular materials, filling ratios, particle size, and shape, etc. Out of all these factors, the type of granular materials used to design a particle damper plays a major role. Therefore, this contribution aims to investigate the influence of eleven different granular materials on vibration attenuation. Furthermore, the application of particle dampers for reducing the low‐frequency vibration amplitude of a wind turbine generator has been demonstrated. For this, two different approaches, namely the damping plate concept and the existing cavity concept have been introduced. It has been found that both concepts are capable of reducing the vibration amplitude tremendously. The material investigation has shown that rubber granulate can reduce the vibration amplitude of the test specimen significantly higher in comparison to the other materials by increasing the additional mass to the entire system marginally. The material test is independent of any particular application. Hence, the results can be used to reduce the vibration amplitude of any mechanical structure.

Модель нелінійного деформування зернистих композитів

The model of nonlinear deformation of a granular composite material of a stochastic structure with physically nonlinear components was constructed. The basis is the stochastic differential equations of the physically nonlinear theory of elasticity by L.P. Khoroshun. The solution to the problem of the stress-strain state and effective deformable properties of the composite material is built using the averaging method. An algorithm for determining the effective properties of granular material with physically nonlinear components has been developed. The solution of nonlinear equations, taking into account their physical nonlinearity, is constructed by the iterative method. The law of the relationship between macrostresses and macrostrains in granular material and the dependence of average strains and stresses in its components on macrostrains has been established. Curves of deformation of the material were constructed for different values of the volume content of its components. The dependence of the effective deformable properties of the granular material on the volume content of the components was studied. The effect of component nonlinearity on the deformation of granular composite material was studied. It was established that the nonlinearity of the components significantly affects the effective deformable properties and the stress-strain state of granular materials.

Modelling of water droplet dynamics on hydrophobic soils: a review

The hydrophobicity of soils (or soil water repellency) can be naturally promoted by wildfires or synthetically induced by hydrophobic compounds (polydimethylsiloxane, tong oil, etc.). Soil phenomena can be related to hydrophobicity, such as soil erosion (splash erosion and rill erosion) and post-wildfire debris flows. The hydrophobicity of soils is characterized by the contact angle, and the interactions between water droplet and solid particles including spreading, oscillation, and infiltration. Early studies on soil water repellency mainly focus on the experimental aspects, while with the development of advanced numerical tools, numerical methods have been widely applied to study the hydraulic properties of hydrophobic granular materials in recent years. This paper comprehensively investigates the different numerical methods for modelling the interaction between water droplets and hydrophobic soils, i.e., smoothed particle hydrodynamics (SPH), lattice Boltzmann method (LBM), material point method (MPM), and volume of fluid (VOF). The features of different method are summarized, and the future work are discussed.

Investigation of the flow characteristics of spherical harmonic particles using the level set method

Non-spherical granular flow is critical for hopper design and applications. Although particle morphology has an evident influence on the dynamic properties of granular materials, a large number of numerical simulations contribute to the dynamic behaviors of convex particles. In this work, concave particles are represented using the spherical harmonic functions, and the accurate collision forces between spherical harmonics particles are obtained by the level set algorithm. Subsequently, the influences of particle sphericity, shape parameters, and hopper angles on the mass flow rate, flow fluctuation, mass flow index, particle velocity, and inter-particle contact forces of spherical harmonics particles are investigated using the discrete element method. Results indicate that spherical harmonic particles with small sphericity and large shape parameters have dense clusters and strong interlocking, which cause larger normal contact forces between particles. As a result, spherical harmonic particles have lower flow rates and more significant flow fluctuations than spheres. • Concave particles are constructed by the spherical harmonic functions. • Contact forces between concave particles are calculated by the level set method. • The flow properties of spherical and concave particles in the hopper are compared. • Concave particles have lower flow rates and larger flow fluctuations than spheres. • The contact forces between concave particles increase with decreasing sphericity.

Damping performance of particle dampers with different granular materials and their mixtures

A particle damper is a passive vibration control technology that utilizes the high damping properties of granular materials for reducing the vibration amplitude of a structure over a wide frequency range. Energy dissipation of particle damper is a highly nonlinear and complex physical phenomenon [1]. Previous studies have shown that the damping mechanism of a particle damper depends on several factors, like particle size and shape, granular material, filling ratio, and the number of particles [2–5]. Out of these parameters, the type of granular material used in the particle damper plays a major role in reducing the vibration amplitude of a mechanical structure. Therefore, the current contribution aims to investigate the influence of 20 different granular materials on vibration attenuation. The granular materials under investigation are subdivided into two major groups, namely: soft particles, like rubber granulate, and hard particles, like steel balls. Furthermore, this paper proposes a hybrid particle damper in which two different types of granular material mixtures are used, i.e. a particle damper in which for instance soft particles are mixed with hard particles. Moreover, in this contribution, fine particles, like rubber powder are mixed with hard granular materials like lead shot, which can be seen as an extension of the fine particle impact damper concept [6]. The humidity-dependent behavior of particle dampers is also another important issue, which is addressed in this paper. To investigate the vibration attenuation efficiency of all the granular materials and their mixtures including the humidity-dependent behavior, a laser scanning vibrometer device is used. Generally, the relationship between the vibration response and the granular material mass is rarely addressed in the literature, which can restrict the industrial application of particle dampers. Hence, the additional mass of the granular material is also a focus of this paper. The experimental investigation shows that the vibration response of the test specimen is significantly lower for particles with lower densities in the low-frequency range. Furthermore, an excellent damping efficiency can be also observed for the particle damper with a granular material mixture. The results obtained in this study are not restricted to any special structure and can be implemented in several industrial applications, where vibration and noise attenuation plays a major role, like automotive, aerospace, wind turbine, medical technology, mining, etc.

Mechanical properties of unbound granular materials reinforced with nanosilica

The development of new technologies for soil improvement has been a hot research topic in the fields of geological engineering, geotechnical engineering, and road engineering. Nanomaterials have been proven to offer significant advantages in the field of geotechnical material enhancement due to their unique structures and excellent properties. The effect of nanosilica amount on the stress-strain behavior, elastic modulus, shear strength, and shear parameters of unbound granular materials was investigated, and its potential enhancement mechanism was discussed in this research. Treated samples with nanosilica contents (by weight) of 0,1%, 2%, 3%, 3.5%, 4%, and 4.5% were prepared and rigorously examined through unconsolidated undrained (UU) triaxial tests under different confining pressures. Also, the intrinsic mechanism and variations in the microstructure of the specimens were investigated by the computed tomography (CT) and scanning electronic microscope (SEM). Testing results showed that with the addition of more nanosilica, the elastic modulus and shear strength of the specimens increased and the ductility decreased. The apparent cohesion of the treated specimens increased approximately linearly and had almost as little effect on the internal friction angle. The maximum improvement rate was obtained at 3.5% of nanosilica content. The CT and SEM scanning results indicated that the control specimen has a higher void ratio than the treated specimens, and the filling and nucleation effects of nanomaterials may be the intrinsic mechanism to improve the mechanical properties of unbound particulate materials. The experimental results contribute to enriching the application of nanomaterials in geotechnical engineering, guiding the optimization of mechanical properties of unbound granular materials.