A hybrid approach for modeling of breakable granular materials using combined finite-discrete element method

It is well known that particle breakage plays a critical role in the mechanical behavior of granular materials and has been a topic subject to intensive studies. This paper presents a three dimensional fracture model in the context of combined finite-discrete element method (FDEM) to simulate the breakage of irregular shaped granular materials, e.g., sands, gravels, and rockfills. In this method, each particle is discretized into a finite element mesh. The potential fracture paths are represented by pre-inserted non-thickness cohesive interface elements with a progressive damage model. The Mohr–Coulomb model with tension cut-off is employed as the damage initiation criterion to rupture the predominant failure mode at the particle scale. The particle breakage modeling using combined FDEM is validated by the qualitative agreement between the results of simulated single particle crushing tests and those obtained from laboratory tests and prior DEM simulations. A comprehensive numerical triaxial tests are carried out on both the unbreakable and breakable particle assemblies with varied confining pressure and particle crushability. The simulated stress–strain–dilation responses of breakable granular assembly are qualitatively in good agreement with the experimental observations. The effects of particle breakage on the compressibility, shear strength, volumetric response of the fairly dense breakable granular assembly are thoroughly investigated through a variety of mechanism demonstrations and micromechanical analysis. This paper also reports the energy input and dissipation behavior and its relation to the mechanical response.     

Analysis of the influence of crushing on the behavior of granular materials under shear

The behavior of granular materials mainly depends on the mechanical and engineering properties of particles in its structural matrix. Crushing or breakage of granular materials under compression or shear occurs when the energy available is sufficient to overcome the resistance of the material. Relatively little systematic research has been conducted regarding how to evaluate or quantify particle crushing and how it effects the engineering properties of the granular materials. The aim of this study is to investigate the effect of crushing on the bulk behavior of granular materials by using manufactured granular materials (MGM) rather than using a naturally occurring cohesionless granular material. MGM allow changing only one particle parameter, namely the “crushing strength”. Four different categories of MGM (with different crushing strength) are used to study the effect on the bulk shear strength, stiffness modulus, friction and dilatancy angle “engineering properties”. A substantial influence on the stress–strain behavior and engineering properties of granular materials is observed. Higher confining stress causes some non-uniformity (strong variations/jumps) in volumetric strain and a constant volumetric strain is not always observed under large shear deformations due to crushing, i.e. there is no critical state with flow regime (with constant volumetric strain).     

Breakage of an artificial crushable material under loading

The mechanical behaviour of granular materials depends on their grading. Crushing of particles under compression or shear modifies the grain size distribution, with a tendency for the percentage of fine material to increase. It follows that the frictional properties of the material and the critical states are modified as a consequence of the changes in grain size distribution and the available range of packing densities. This paper illustrates an extended experimental investigation of the evolution of the grading of an artificial granular material, consisting of crushed expanded clay pellets under different loading conditions. The changes of grading of the material after isotropic, one-dimensional and constant mean effective stress triaxial compression were described using a single parameter based on the ratio of the areas under the current and an ultimate cumulative particle size distribution, which were both assumed to be consistent with self similar grading with varying fractal dimension. Relative breakage was related to the total work input for unit of volume. For poorly graded samples, the observed maximum rate of breakage is practically independent of initial uniformity. Further experiments at higher confining stress are required to investigate the mechanics of breakage of better graded samples.     

堆石料真三轴条件下力学特性试验研究进展

该文综述了国内外岩土真三轴仪的发展、堆石料力学特性及机理相关的研究现状。重点介绍了该研究团队开发的大型岩土静动真三轴试验机及在堆石料力学特性试验研究方面取得的初步成果。按加载方式,土的真三轴仪可以分为3类：刚性加载真三轴仪、柔性加载真三轴仪和混合型加载真三轴仪。堆石料真三轴试验具有试样尺寸大、承压高、各方向相互干扰强、试样变形后荷载对中难、加压板与试样间摩擦效应强、试样安装和量测复杂等诸多困难。因而,目前适用于堆石料的真三轴仪和试验成果均较少。考虑堆石料真三轴及复杂应力路径条件下的颗粒破碎、各向异性等,研究其力学特性并开发相应的本构模型是该课题发展的趋势。清华大学大型岩土静动真三轴试验机中联合采用了椭圆形试样帽和异形乳胶膜的封样方式,可很好地解决真三轴试样的高压密封、拆装、量测和耐久性等一系列难题。对堆石料进行了一系列真三轴复杂应力路径试验,结果表明真三轴试验中堆石料表现出更明显的应力诱导各向异性和应力状态依赖性,特别是对小主应力-应变关系、球应力-体应变关系和广义剪应力-剪应变关系的影响更显著。球应力和广义剪应力对体积应变和广义剪应变之间存在着明显的交叉影响。     

Evolution of particle breakage and volumetric deformation of binary granular soils under impact load

Binary granular soils, mixtures of carbonate sands and nonplastic fines, are widely used for constructions of foundation, airport and embankment in island and coast. Impact load (e.g., sea wave, aircraft landing, pile driving and dynamic compaction during foundation, et al.) is frequently exerted to the mixtures. It is therefore of extreme importance to investigate the evolutions of particle size distribution, particle breakage and volumetric deformation of the mixtures under impact load due to that the grains of carbonate sands are easily to be crushed, which may significant affect its mechanical behavior. Three mixtures (i.e., 100% carbonate plus 0% fines (by dry weight), 90% carbonate plus 10% fines and 80% carbonate plus 20% fines) were prepared to analyze the effect of fines content on particle breakage and volumetric deformation under impact load. It was observed that a unique fractal grading could be obtained for all the mixtures when the blow number was large enough (\(N>20,000\)). The void ratio of the mixtures converged to be a constant ultimate value as the mixture reached the fractal state. The volumetric strain and relative particle breakage with respect to the blow number could be described by hyperbolic functions, indicating that the volumetric strain and relative particle breakage progressively increased to ultimate values with increasing the blow number.     

不同应力路径下堆石料的动力变形特性试验研究

采用大型多功能静动三轴试验机,对堆石料分别进行了常规三轴循环加载、等p循环加载和等q循环加载三种不同应力路径下的动力变形试验研究,探讨了不同应力路径下围压﹑固结应力比及动应力比等因素对体应变和偏应变的影响规律及其变形机制。试验结果表明：在循环荷载作用下,不同应力路径对堆石料体应变和偏应变的发展规律影响较大;在等p循环加载作用下引起的往返体应变为负值,即发生剪胀现象,且在轴向剪切时达到最大剪胀值,反向剪切时基本不发生剪胀;在等q循环加载作用下产生较大的残余体应变和残余偏应变,两者均不可忽略不计,主要与堆石料的各向异性和颗粒破碎有关。     

Discrete element simulation of ballast and gravel under special consideration of grain-shape,grain-size and relative density

A particle based numerical simulation procedure is presented, which allows the reproduction of the stress-strain characteristics of stiff granular material (ballast or gravel) under quite different loading conditions. If grain-shape, grain-size and relative density is considered in a proper manner, a relatively simple constitutive law with only three constants (friction coefficient, shear and normal stiffness) is sufficient for the reproduction of the observed stress-deformation behaviour. The paper describes the procedures, how to get information about grain-shape and size and how to generate samples with realistic grain-shape, size and relative density under the pre-requisite to optimize the computational effort. The procedure was successfully tested using five different lab test: soil-dump test, soil-pouring test, oedometer test, triaxial test and multi-stage shear test, also under consideration of different initial densities.     

Use of CFD-DEM to evaluate the effect of intermediate stress ratio on the undrained behaviour of granular materials

This study investigates the effect of intermediate stress ratio (b) on the mechanical behaviour of granular soil in true triaxial tests. A CFD-DEM solver with the ability to model compressible fluid and moving mesh has been developed and calibrated based on existing experimental test results on Nevada sand. The effect of b on the undrained true triaxial test, which has been neglected in the literature, was investigated using a reasonable number of models. The effects of the initial confining stress and initial void ratio also have been studied. The developed model was used to calculate the hydrodynamic forces on the particles and evaluate the ratio of the particle–fluid interaction force to the resultant force on the particles. It has been demonstrated that, in numerical studies, the effect of these forces cannot be neglected.     

DEM simulations of stiff and soft materials with crushable particles: an application of expanded perlite as a soft granular material

The mechanical behavior of granular materials is largely affected by particle breakage. Physical and mechanical properties of granular materials, such as grain size distribution, deviatoric and volumetric behavior, compressibility and mobilized friction angle are affected by particle crushing. This paper focuses on the evolution of the above mentioned characteristics using the Discrete Element Method (DEM). Behaviors of stiff and soft materials are studied using well established crushing criteria. Results from simulations indicate that stiff materials, have a typical fractal distribution of particle size, which is dominant when confining pressure increases. The fractal characteristic parameter of grain size effect is discussed. Evolution of shear stresses and volumetric strains during shearing are also predicted and analyzed. Expanded perlite, selected as a soft material, is investigated in terms of shear and volumetric behavior. For perlite, triaxial compression tests and corresponding DEM simulations are also performed. Results show good agreement between experiments and simulations and support the fact that the DEM can be considered as a useful tool to predict the behavior of crushable granular materials.     

HotQC simulation of nanovoid growth under tension in copper

We apply the HotQC method of Kulkarni et al. (J Mech Phys Solids 56:1417–1449, 2008) to the study of quasistatic void growth in copper single crystals at finite temperature under triaxial expansion. The void is strained to 30% deformation at initial temperatures and nominal strain rates ranging from 150 to 600 K and from 2.5 × 10⁵ to 2.5 × 10¹¹s⁻¹, respectively. The interatomic potential used in the calculations is Johnson’s Embedded-Atom Method potential Johnson (Phys Rev B 37:3924–3931, 1988). The computed pressure versus volumetric strain is in close agreement with that obtained using molecular dynamics, which suggests that inertia effects are not dominant for the void size and conditions considered. Upon the attainment of a critical or cavitation strain of the order of 20%, dislocations are abruptly and profusely emitted from the void and the rate of growth of the void increases precipitously. Prior to cavitation, the crystal cools down due to the thermoelastic effect. Following cavitation dislocation emission causes rapid local heating in the vicinity of the void, which in turn sets up a temperature gradient and results in the conduction of heat away from the void. The cavitation pressure is found to be relatively temperature-insensitive at low temperatures and decreases markedly beyond a transition temperature of the order of 250 K.     

DEM modeling of shear bands in crushable and irregularly shaped granular materials

A method of modeling convex or concave polygonal particles is proposed. DEM simulations of shear banding in crushable and irregularly shaped granular materials are presented in this work. Numerical biaxial tests are conducted on an identical particle assembly with varied particle crushability. The particle crushing is synchronized with the development of macroscopic stress, and the evolution of particle size distribution can be characterized by fractal dimension. The shear banding pattern is sensitive to particle crushability, where one shear band is clearly visible in the uncrushable assembly and X-shaped shear bands are evident in the crushable assembly. There are fewer branches of strong force chains and weak confinement inside the shear bands, which cause the particles inside the shear bands to become vulnerable to breakage. The small fragments with larger rotation magnitudes inside the shear bands form ball-bearing to promote the formation of shear bands. While there are extensive particle breakages occurring, the ball-bearing mechanism will lubricate whole assembly. With the increase of particle crushability the shear band formation is suppressed and the shear resistance of the assembly is reduced. The porosity inside the shear bands are related to the particle crushability.     

Study of the shear behavior of binary granular materials by DEM simulations and experimental triaxial tests

This paper aims at studying the shear behavior of mixtures of fine and coarse particles by classical triaxial tests. The work is performed both on experimental tests and computer simulations by discrete element method. The comparisons between experimental and simulation results on monosized and binary samples show that the DEM model can reproduce deviatoric curves satisfactorily in experimental conditions. The shear behavior of monosized and binary systems with the same initial void ratio differs significantly, suggesting that the state of compaction of the system is more influential than the initial void ratio. Comparison between compacted and uncompacted samples confirms that compaction increases the shear strength of granular matter. At the particle scale, the coordination number decreases with the augmentation of the volume fraction of coarse particles. The average rotation velocity of fine particles is higher than coarse particles, but their particle stress tensor is smaller than coarse ones.     

The role of contact friction in the dynamic breakage behavior of granular materials

Based on the discrete element method, a multi-scale model is employed to investigate the role of contact friction in the dynamic compression responses of brittle granular materials. Four numerical granular samples with different particle friction coefficients ranging from 0.0 to 2.0 are tested and the particle breakage extent is quantified with the Einav breakage index. It is observed that the relationship of the breakage extent with the axial stress is apparently non-monotonic concerning the particle friction coefficient. At the same stress level, the breakage extent exhibits a minimum when the particle friction coefficient is around 0.1 but increases significantly with the particle friction coefficient to both sides. The micro physical origin of this non-monotonic behavior is a distinct transition in dominant particle-breakage modes from tension to shear. Moreover, energy analyses also show non-monotonic evolution of the frictional and damping dissipation with the particle friction coefficient. The joint effect of these two dissipation terms contributes to the non-monotonic behavior of particle breakage. In addition, the accuracy and competence of two frequently-used micro quantities, fraction of sliding contacts and average coordination number, are discussed.

     

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.     

Stochastic process of fracture in granular materials

By regarding the coefficient of particle friction of granular materials as a random variable distributed on the particle surface, the mechanism of particle sliding is interpreted as a stochastic process. Axial, shearing and volumetric strains are defined with regard to the deformation of a microscopic regular assembly of uniform spheres. For illustration, these strains are calculated for a uniform distribution of the coefficient of particle friction and applied to some triaxial test results reported elsewhere.     

A discrete model for simulating shear strength and deformation behaviour of rockfill material, considering the particle breakage phenomenon

This study focuses on numerical modelling of rockfill material with the discrete element method (DEM). This method was used due to the special features of rockfill material, such as intense particle breakage and high contracting behaviour, which are inherently due to large particle size. Because the DEM models the interaction of separate elements, it is capable of modelling discrete structures of granular materials and particle breakage. The model used in this study uses PFC^2D and considers breakable clumps. To validate the presented model for rockfill material, numerical single crushing tests and triaxial tests on the Purulia dam’s material were simulated. Due to the size-dependant crushing strength being involved in the breakage criterion, and also considering particle confinement, size-dependant and stress level-dependant behaviour was successfully simulated on modelled rockfill material. The variation of the sample’s particle grading from before the biaxial tests and after shear failure occurred was reported. The obtained results demonstrate the accuracy of the adopted model and the model’s capability for considering a rockfill material’s strength, deformation and crushing behaviour.     

Fabric characterisation in transitional soils

A “transitional” mode of soil behaviour implies that dense and loose samples do not converge towards the same volumes within the strains and stresses applied by simple oedometer and triaxial tests. As this behaviour involves soils with different gradings and mineralogies (e.g. gap graded, well graded and/or mixed mineralogies), identifying the factors responsible is difficult. Nevertheless, it has been previously speculated that strong forms of fabric that are difficult to break down as strains and stresses are applied, might be the common cause. This paper aims at investigating some elements of fabric at the microscale of transitional soils. A gap graded and two well graded mixtures with large amounts of non-plastic fines were investigated by oedometer and triaxial tests. As it would be difficult to identify experimentally many commonly used elements of fabric in these soils, e.g. the contact network, mercury intrusion porosimetry was used as a first step to characterise the evolution of pore size distributions (PSDs) of dense and loose samples undergoing the same stress paths, using the PSDs as a proxy of fabric. Multi-directional bender element testing was performed to confirm the isotropy of the elastic stiffness, from which it might be inferred that the fabric is also isotropic. Statistical parameters of the PSDs were calculated, the changes of which were related to the evolution of macroscale void ratios. The robust fabrics causing lack of convergence were characterised by a complex evolution of the PSDs, the initial differences of which could not be erased during conventional testing. This work also provided a simple method to examine the fabric of particularly well graded or gap graded materials, for which other techniques, such as CT or SEM, could not reveal the multi-scale nature of the fabric.     

Probing into the strain induced anisotropy of Hostun RF loose sand

Several recent linear drained preloading histories with fixed direction were especially designed to study the effects of strain induced anisotropy of loose Hostun RF sand in the compression side of the classical triaxial plane. Nearly identical void ratio and a same initial isotropic stress state prior to the final undrained shearing in compression are the requirements of the experimental program to take into account only the deviatoric strain histories. The effects of previous deviatoric strain histories on the undrained response of loose Hostun RF sand are identified: mainly the progressive transformation of a contractive and unstable behaviour of very loose sand into a dilative and stable behaviour of dense-like sand by previous linear drained history, while remaining in the same state of loose density. Experimental data evidence the directional dependency of the initial gradient of the effective stress paths, independent of the length of the approaching linear stress paths; the large common non linear effective stress response up to the deviatoric stress peak; the progressive appearance of the dilatancy domain and the unexpected evolution of the undrained behaviour of loose and presheared sand. The paper provides new insights into the mechanisms of strain induced anisotropy of loose sand created by simple linear triaxial stress paths from an isotropic stress state.     

A laboratory investigation on an undisturbed silty sand from a slope prone to landsliding

A laboratory investigation is presented for undisturbed samples of a silty sand under saturated conditions. The soil was sampled from test pits south of Rüdlingen in North–East Switzerland, where a landslide triggering experiment was carried out on a steep forest slope. The aim of the work was to characterise the behaviour of the soil in triaxial tests, in the light of the possible failure mechanisms of the slope. Conventional drained and undrained triaxial tests were conducted to detect critical state conditions as well as peak shear strength as a function of confining pressure. Soil specimens were also exposed to stress paths simulating in situ water pressure increase to study the stress–strain response and to enhance the ability to predict failure conditions more accurately in the future. Possible unstable response along the stress paths analysed was investigated by means of second order work and strain acceleration. The results show that temporary unstable conditions may be encountered for this soil at stress ratios below ultimate failure and even below critical state line, depending on void ratio, drainage conditions and time dependent compressibility. A modified state parameter is explored as a potentially useful tool to discriminate conditions leading to eventual collapse.     

碎石料应力路径大型三轴试验的离散元模拟研究

碎石料在高填方工程中得到广泛应用。由于其粒径较大,对碎石料力学特性的研究通常需要大型的试验设备。该文探索通过离散元数值模拟方法研究碎石料的应力路径相关力学特性。离散元程序可以将若干球形单元粘结成一个捆绑单元,从而模拟可破碎的碎石颗粒。该文首先简要介绍了离散元的计算原理、特点和模拟过程,并建立碎石料试件的离散元模型。通过对比一组恒定围压下的大型三轴试验,确定了各参数,对所建模型进行了标定。进而通过该模型独立预测碎石料试件在三种不同应力路径加载时的应力-应变关系及体变特性,并与相应的应力路径大型三轴试验结果进行对比,验证了离散元方法可以较为准确地计算碎石料沿不同应力路径加载时的力学特性,同时还讨论了碎石料的小应变刚度特性。