Showing papers in "Granular Matter in 2016"

Microstructure evolution of granular soils in cyclic mobility and post-liquefaction process

Abstract: Understanding the evolution of microstructure in granular soils can provide significant insights into constitutive modeling of soil liquefaction. In this study, micromechanical perspectives of the liquefaction process are investigated using the Discrete Element simulation. It is observed that during various stages of undrained cyclic loading, the soil exhibits definitive change in the load-bearing structure, indicated by evolution of the coordination number and non-affine displacements. A new particle-void fabric, termed as “centroid distance”, is also proposed to quantify the evolution of particles and voids distribution in the granular packing. The fabric index is found to have strong correlation with cyclic mobility and post-liquefaction deformation of granular soils. Evolution of the fabric index indicates that particles and voids redistribute irreversibly before and after liquefaction. A highly anisotropic particle-void structure and loading-bearing capacity can be formed in the post liquefaction stage.

Numerical and experimental verification of a damping model used in DEM

Abstract: This paper presents a study on the damping ratio $$({\upbeta })$$ used in discrete element simulations. Physical experiments are performed by dropping particles from a predetermined height. Two kinds of granular particles, aluminum and steel spheres, are used. The size of these particles are the same. The process of particle depositing under gravity is simulated using the discrete element method. The experimental observation is compared with the numerical result to identify the appropriate $${\upbeta }$$ . The result indicates that the appropriate damping ratio used in discrete element simulations is between 0.2 and 0.3 %. Various $${\upbeta }$$ are then used in the numerical simulations to study the effect of $${\upbeta }$$ on the dropping process. The final height of the sample relates to $${\upbeta }$$ and the drop height. The effect of $${\upbeta }$$ is more profound for small drop height. For greater drop height, the effect of $${\upbeta }$$ is negligible.

A coupled discrete element-finite difference model of selective laser sintering

Abstract: Selective laser sintering (SLS) is an additive manufacturing technology whereby one can 3D print parts out of a powdered material. However, in order to produce defect free parts of sufficient strength, the process parameters (laser power, scan speed, powder layer thickness, etc.) must be carefully optimized depending on material, part geometry, and desired final part characteristics. Computational methods are very useful in the quick optimization of such parameters without the need to run numerous costly experiments. Most published models of this process involve continuum-based techniques, which require the homogenization of the powder bed and thus do not capture the stochastic nature of this process. Thus, the aim of this research is to produce a reduced order computational model of the SLS process which combines the essential physics with fast computation times. In this work the authors propose a coupled discrete element-finite difference model of this process. The powder particles are modeled as discrete, thermally and mechanically interacting spheres. The solid, underneath substrate is modeled via the finite difference method. The model is validated against experimental results in the literature and three-dimensional simulations are presented.

The influence of fines content and size-ratio on the micro-scale properties of dense bimodal materials

Abstract: This paper considers factors influencing the fabric of bimodal or gap-graded soils. Discrete element method simulations were carried out in which the volumetric fines content and the size ratio between coarse and fine particles were systematically varied. Frictionless particles were used during isotropic compression to create dense samples; the coefficient of friction was then set to match that of spherical glass beads. The particle-scale data generated in the simulations revealed key size ratios and fines contents at which transitions in soil fabric occur. These transitions are identified from changes in the contact distributions and stress-transfer characteristics of the soils and by changes in the size of the void space between the coarse particles. The results are broadly in agreement with available experimental data on minimum void ratio and contact distributions. The results have implications for engineering applications including assessment of the internal stability of gap-graded soils in embankment dams and flood embankments.

Memory of jamming–multiscale models for soft and granular matter

Abstract: Soft, disordered, micro-structured materials are ubiquitous in nature and industry, and are different from ordinary fluids or solids, with unusual, interesting static and flow properties. The transition from fluid to solid - at the so-called jamming density - features a multitude of complex mechanisms, but there is no unified theoretical framework that explains them all. In this study, a simple yet quantitative and predictive model is presented, which allows for a variable, changing jamming density, encompassing the memory of the deformation history and explaining a multitude of phenomena at and around jamming. The jamming density, now introduced as a new state-variable, changes due to the deformation history and relates the system's macroscopic response to its micro-structure. The packing efficiency can increase logarithmically slow under gentle ``tapping'' or repeated (isotropic) compression, leading to an increase of the jamming density. In contrast, shear deformations cause anisotropy, changing the packing efficiency exponentially fast with either dilatancy or compactancy. The memory of the system near jamming can be explained by a micro-statistical model that involves a multiscale, fractal energy landscape and links the microscopic particle picture to the macroscopic continuum description, providing a unified explanation for the qualitatively different flow-behavior for different deformation modes. To complement our work, a recipe to extract the history-dependent jamming density from experimentally accessible data is proposed, and alternative state-variables are compared. The proposed simple, usable macroscopic model, will help understanding, predicting and avoiding failure of structures or geophysical hazards, and will bring forward industrial process design and optimization, and help solving scientific challenges in fundamental research.

Discrete element simulation of railway ballast: modelling cell pressure effects in triaxial tests

Abstract: The paper investigates reproducing the effects of confining pressure on the behaviour of scaled railway ballast in triaxial tests in discrete element models (DEM). Previous DEM work, using a standard Hertzian elastic contact law with an elastic–perfectly plastic tangential slip model, has been unable to replicate the behaviour observed in laboratory tests across a range of confining pressures without altering both the material stiffness and the inter-particle friction. A new contact law modelling damage at the contacts between particles is introduced. Particle contact is via spherically-capped conical asperities, which reduce in height if over-stressed. This introduces plasticity to the behaviour normal to the contact surface. In addition, the inter-particle friction angle is varied as a function of normalized contact normal force. At relatively low normal forces the friction angle must be increased for peak mobilized friction angles to match the laboratory data, an effect that is attributed to interlocking at the scale of surface roughness. Simulation results show close agreement with laboratory data.

DEM analysis of the size effects on the behavior of crushable granular materials

Abstract: Four sets of individual-particle crushing tests were carried out on sandstone grains of different size with geometric similarity. The tensile strength was analyzed using Weibull statistics, and the size-hardening law was obtained. The experimental data also validated that the Weibull modulus is independent of the grain size. Considering both the shear and tensile fracture modes of the particle, the Mohr–Coulomb model with a tension cut-off was employed as the fracture criterion of a single particle. When the particle stresses satisfied the fracture criterion, three new fragments modeled by the ‘clump’ were generated to replace the broken particle. Nine spheres with four different sizes were released from the clump and allowed to continue crushing if the fragment stresses fulfilled the criterion again. Two polydisperse assemblies with different particle sizes but same initial fabrics were prepared. DEM simulations of triaxial shear tests with different grain sizes were carried out on the crushable granular material with varied confining pressures. The simulated stress–strain–dilation responses were in agreement with the experimental observations. The macro–micro responses of the two samples, including the stress–strain–dilation behavior, the particle crushing, and the normal contact force distribution, were discussed in detail. The cause of the size effect on the shear strength and deformation was thoroughly investigated through a variety of mechanism demonstrations and micromechanical analysis.

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

Abstract: 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.

Meso-structure evolution in a 2D granular material during biaxial loading

Abstract: Multi-scale approaches of constitutive modeling require an intermediate scale linking the variables in macroscopic scale (incremental stress and strain) to variables in microscopic scale (contact force and contact displacement). In this paper, we introduce a mesoscopic scale, in which the granular material is tessellated into small loops by contact network. Then numerical biaxial tests from different initial states by DEM modeling, is performed to investigate how the meso-structure (mesoscopic loops) evolves along the drained biaxial loading path. Results suggest that the procedure of the biaxial test is accompanied with the exchange between small, dense structures and big, loose structures. The macroscopic dilatancy primarily originates from this exchange. In dense and intermediate specimens the meso-structure evolution is found not to be consistent with the evolution of the macroscopic volumetric strain during contractancy phases. This inconsistency has led to interpret the elastic and the plastic parts of the volumetric strain from a meso-scale viewpoint. It is shown that the initial contractancy in dense and intermediate specimens is largely an elastic process, which is highly dependent on elastic parameters of the material.

Micro origins for macro behavior in granular media

Abstract: We report the latest advances in understanding, characterization and modeling of key micro mechanisms and origins underpinning the interesting and complex macroscopic behavior of granular matter. Included in this Topical Collection are novel theories, innovative experimental tools and new numerical approaches, focusing primarily on three subtopics governing important multiscale properties of granular media: (a) the jamming transition from fluid- to solid-like behavior, critical state flow and wave propagation, (b) the signature of fabric and its evolution for granular media under general loading conditions, and (c) mechanisms like rotation, breakage, failure and aggregation. The significance of these contributions and exploratory future directions pertaining to cross-scale understanding of granular matter are discussed

DEM assessment of scaling laws capturing the grain size dependence of yielding in granular soils

Abstract: Experimental evidences show that the pressure at which granular soils exhibit a sharp increase of their compressibility depends on the size of the particles that constitute their skeleton, thus reflecting the role of micro-scale fracture events on the macroscopic compression of granular systems. In this paper, the distinct element method (DEM) is used to test the validity of scaling laws relating the macroscopic energy at which the grains of a soil matrix crush collectively to the energy at which individual grains subjected to diametrical compression undergo tensile fracture. Oedometric compression tests on uniformly graded specimens with different values of particle size have been simulated by considering two deterministic fracture models and a probabilistic criterion based on the Weibull weakest link theory. It has been shown that the constants of proportionality between grain-scale and assembly-scale crushing thresholds depend considerably on the statistical variability of the particle strength, and that a larger variability exacerbates the departure between the scaling constants pertaining to deterministic and probabilistic models. Nevertheless, for the chosen set of initial conditions and loading paths, the simulations have suggested the applicability of a proportional scaling between the energy stored in the assembly at the moment of yielding and that required to fracture a single grain. In particular, the simulations revealed that the scaling constants relating the microscopic and macroscopic energy thresholds fall within a rather narrow range and do not depend significantly on the grain size. The Breakage Mechanics theory has been used to further explore such connection between length scales, finding a good agreement between the DEM simulations and the yielding stress computed by the theory whenever its parameters were defined on the basis of the scaling constants computed from the DEM model. These results confirm the interplay between the statistical variability of the particle strength and the grain size dependence of the yielding pressure, stressing at the same time the usefulness of energy scaling arguments in incorporating the effect of micro-scale fracture events into continuum models.

Jammed architectural structures: towards large-scale reversible construction

Abstract: This paper takes a first step in characterizing a novel field of research—jammed architectural structures—where load-bearing architectural structures are automatically aggregated from bulk material. Initiated by the group of Gramazio Kohler Research at ETH Zurich and the Self-Assembly Lab at Massachusetts Institute of Technology, this digital fabrication approach fosters a combination of cutting-edge robotic fabrication technology and low-grade building material, shifting the focus from precise assembly of known parts towards controlled aggregation of granular material such as gravel or rocks. Since the structures in this process are produced without additional formwork, are fully reversible, and are produced from local or recycled materials, this pursuit offers a radical new approach to sustainable, economical and structurally sound building construction. The resulting morphologies allow for a convergence of novel aesthetic and structural capabilities, enabling a locally differentiated aggregation of material under digital guidance, and featuring high geometrical flexibility and minimal material waste. This paper considers (1) fundamental research parameters such as design computation and fabrication methods, (2) first results of physical experimentation, and (3) the architectural implications of this research for a unified, material-driven digital design and fabrication process. Full-scale experimentation demonstrates that it is possible to erect building-sized structures that are larger than the work-envelope of the digital fabrication setup.

Micromechanics of seismic wave propagation in granular materials

Abstract: In this study experimental data on a model soil in a cubical cell are compared with both discrete element (DEM) simulations and continuum analyses. The experiments and simulations used point source transmitters and receivers to evaluate the shear and compression wave velocities of the samples, from which some of the elastic moduli can be deduced. Complex responses to perturbations generated by the bender/extender piezoceramic elements in the experiments were compared to those found by the controlled movement of the particles in the DEM simulations. The generally satisfactory agreement between experimental observations and DEM simulations can be seen as a validation and support the use of DEM to investigate the influence of grain interaction on wave propagation. Frequency domain analyses that considered filtering of the higher frequency components of the inserted signal, the ratio of the input and received signals in the frequency domain and sample resonance provided useful insight into the system response. Frequency domain analysis and analytical continuum solutions for cube vibration show that the testing configuration excited some, but not all, of the system’s resonant frequencies. The particle scale data available from DEM enabled analysis of the energy dissipation during propagation of the wave. Frequency domain analysis at the particle scale revealed that the higher frequency content reduces with increasing distance from the point of excitation.

Towards an aggregate architecture: designed granular systems as programmable matter in architecture

Abstract: Aggregate architectures are full-scale spatial formations made from loose granular matter. Especially if the individual grain is custom-designed, the range of behaviours can be calibrated to match a wide range of architectural and structural performance criteria. The aggregate becomes programmable matter. The relevance of loose granular systems for architecture is on the one hand their rapid re-configurability, allowing for a system not to be destroyed but rather to be recycled. On the other hand aggregates per se can be functionally graded either within one and the same particle type or through mixing different particle geometries. This enables the variation of architectural properties throughout one and the same material system, which is one of the core postulates of current architectural design research. However, very few examples of designed granular matter in architecture exist. The results presented here are thus one of the first coherent bodies of comprehensive research in this field compiled over a period of five years. Methodologically aggregate systems challenge conventional architectural design principles: whereas an architect generally precisely defines local and global geometry of a structure, in a designed granular system he can only calibrate the particle geometry in order to tune the overall behaviour of the aggregate formation. Thus new design methods have been developed throughout the research projects, which are informed by the related fields of granular physics and behaviour-based robotics. In this context the article provides an introduction to both designed particle systems and suitable fabrication approaches in an architectural context. Case study projects serve to verify the applicability of the concepts introduced. The research findings are discussed with regards to their practical, methodological and design theoretical contributions. To conclude, further directions of research are highlighted.

Freestanding loadbearing structures with Z-shaped particles

Abstract: Architectural structures such as masonry walls or columns exhibit a slender verticality, in contrast to the squat, sloped forms obtained with typical unconfined granular materials. Here we demonstrate the ability to create freestanding, weight-bearing, similarly slender and vertical structures by the simple pouring of suitably shaped dry particles into a mold that is subsequently removed. Combining experiments and simulations we explore a family of particle types that can entangle through their non-convex, hooked shape. We show that Z-shaped particles produce granular aggregates which can either be fluid and pourable, or solid and rigid enough to maintain vertical interfaces and build freestanding columns of large aspect ratio ( $$>$$ 10) that support compressive loads without external confinement. We investigate the stability of such columns with uniaxial compression, bending, and vibration tests and compare with other particle types including U-shaped particles and rods. We find a pronounced anisotropy in the internal stress propagation together with strong strain-stiffening, which stabilizes rather than destabilizes the structures under load.

Macro deformation and micro structure of 3D granular assemblies subjected to rotation of principal stress axes

Abstract: This paper presents a numerical investigation on the behavior of three dimensional granular materials during continuous rotation of principal stress axes using the discrete element method. A dense specimen has been prepared as a representative element using the deposition method and subjected to stress rotation at different deviatoric stress levels. Significant plastic deformation has been observed despite that the principal stresses are kept constant. This contradicts the classical plasticity theory, but is in agreement with previous laboratory observations on sand and glass beads. Typical deformation characteristics, including volume contraction, deformation non-coaxiality, have been successfully reproduced. After a larger number of rotational cycles, the sample approaches the ultimate state with constant void ratio and follows a periodic strain path. The internal structure anisotropy has been quantified in terms of the contact-based fabric tensor. Rotation of principal stress axes densifies the packing, and leads to the increase in coordination numbers. A cyclic rotation in material anisotropy has been observed. The larger the stress ratio, the structure becomes more anisotropic. A larger fabric trajectory suggests more significant structure re-organization when rotating and explains the occurrence of more significant strain rate. The trajectory of the contact-normal based fabric is not centered in the origin, due to the anisotropy in particle orientation generated during sample generation which is persistent throughout the shearing process. The sample sheared at a lower intermediate principal stress ratio $$(b=0.0)$$ has been observed to approach a smaller strain trajectory as compared to the case $$b=0.5$$ , consistent with a smaller fabric trajectory and less significant structural re-organisation. It also experiences less volume contraction with the out-of plane strain component being dilative.

Effects of particle size ratio on the macro- and microscopic behaviors of binary mixtures at the maximum packing efficiency state

Abstract: The effects of particle size ratio on the mechanical behaviors of binary mixtures are investigated using three-dimensional discrete element method. The samples with three types of particle size ratios (SR, $$\hbox {SR}=3.0$$ , 4.5 and 6.0) are prepared at the maximum packing efficiency state, which appears at 70 % of the large particle volume content. The results demonstrate that the maxima of peak deviator stress are obtained at the sample with $$\hbox {SR}=4.5$$ . The initial elastic modulus, $$E_{0}$$ , increases with increasing SR. The value of deviator stress increases with increasing SR at the softening stage, whereas an opposite trend is observed at the critical state. The evolutions of the effective particle ratio can capture the differences among the evolutions of the deviator stress of different samples during the softening stage and the critical state to some degree. In addition, different SRs generate different packing structures of the binary mixtures and have apparent influences on the force chain networks in the binary mixtures. With increasing SR, the strong force chains become stronger, and the weak force chains become weaker. The deviator stress contributed by the contacts between large particles and between large and small particles constitutes a major part of the overall deviator stress of the binary mixtures at the maximum packing efficiency state. Furthermore, the positions of the critical state lines of binary mixtures in the $$p-q$$ plane and $$v-\ln p$$ plane are sensitive to SR, and the lubrication effect of small particles in the binary mixtures is enhanced with increasing SR.

Experimental and numerical investigations of dissipation mechanisms in particle dampers

Abstract: Particle dampers are passive devices allowing strong damping of structures vibrating in harsh environment. We investigate the energy dissipation in a rigid enclosure attached to a shaker and partially filled with particles. Our experiments match an analytical description, which we corroborate then with discrete element method simulations. We show that the loss factor does not depend on the material of the particles or their number, but heavily relies on the total mass of the embedded grains and on the driving magnitude only. Our measurements reveal the contribution of the viscous flow of air surrounding the grains to the overall loss factor of the dampers.

Critical state behaviors of a coarse granular soil under generalized stress conditions

Abstract: Critical state line (CSL) is the central concept in soil mechanics. A series of true triaxial compression tests under the constant- $${p}'$$ and constant-b loading condition were carried out to investigate the CSL of a coarse granular soil. It was observed that the intermediate principal stress ratio (i.e., the b-value) greatly influenced the CSLs in both $$q{-}{p}'$$ and $$e{-}{p}'$$ spaces. The CSL slope in the $$q{-}{p}'$$ space decreased with an increase in b-value. The intercept and gradient of the CSL in the $$e{-}{p}'$$ space decreased with increasing b-value. CSLs incorporating the effects of the b-value in $$q{-}{p}'$$ and $$e{-}{p}'$$ spaces were extended to three-dimensional critical state surfaces (TCSSs) in $$q{-}{p}'{-}b$$ and $$e{-}{p}'{-}b$$ spaces. Two empirical equations were proposed for the two TCSSs in $$q{-}{p}'{-}b$$ and $$e{-}{p}'{-}b$$ spaces, respectively. The predictions by the two equations were in good agreement with the corresponding experimental data. The relationship between the excess friction angle (the difference between the peak state and critical state friction angles) and initial state parameter was influenced by the b-value. However, the relationship between the maximum dilatancy and initial state parameter was independent of the b-value.

Geometrical parameters of binary granular mixtures with size ratio and volume fraction: experiments and DEM simulations

Abstract: Binary mixtures represent the simplest case of polydisperse particulate systems which exhibit interesting and, in some cases, incomprehensive behavior. In this study, experimental and numerical investigations were conducted to examine the effect of particle size ratio and the ratio of volume fraction comprising small particles to the volume of all spheres (volume fraction) on geometrical properties of binary granular mixtures. The size ratio was chosen not smaller than 0.4 to prevent small particles from percolating through bedding and be trapped in the tetrahedron or octahedron made with large contacting spheres. Both, numerical tests and experiments showed an increase in the influence of the volume fraction of small particles on packing density in binary mixtures with an increasing ratio between small and large particles’ diameters. In packings with the particle size ratio not larger than 0.7, the solid fraction reached maximum when the volume fraction of small spheres was 0.6, which was not observed in samples with higher degree of particle size homogeneity. The average coordination number and packing density followed the same paths with the increasing contribution of small particles in mixtures, indicating a strong relationship between parameters. Detailed analysis of the coordination numbers for contacts between different types of particles showed that, average coordination number in binary mixtures was determined mainly by contacts between large and small particles. The composition of bidisperse samples was also found to strongly affect their spatial structure described in this study by means of the radial distribution function.

A corner preserving algorithm for realistic DEM soil particle generation

Abstract: An efficient particle clump generation algorithm for use in discrete element methods (DEMs) was developed to simulate actual particles in a granular specimen The algorithm requires many fewer circles than existing methods, particularly for angular particles The procedure is a logical extension of a computational method for determining the classic Wadell particle roundness in which circles are fitted to the corners of particles Hence, the new method perfectly preserves the location, size and shape of particle corners and is appropriately termed the corner preserving algorithm The remaining perimeter of the particle, which includes concave and flat sections, is fitted with non-corner circles Unlike earlier methods, the corner preserving algorithm requires only a single control parameter to generate the circles This parameter is the ratio of the clump area to the original particle area, AR An algorithm seeks a corresponding optimum clump roughness that achieves the user-prescribed AR The method can easily be incorporated in existing soil particle characterization systems in which binary images or even images of particle assemblies are produced Examples illustrate the simplicity and advantages of the corner preserving algorithm for DEM clump generation

Quasi-static collapse of two-dimensional granular columns: insight from continuum modelling

Abstract: We investigate numerically the mechanism governing the quasi-static collapse of two-dimensional granular columns using a recently proposed continuum approach, the particle finite element method (PFEM), which inherits both the solid mathematical foundation of the traditional finite element method and the flexibility of particle methods in simulating ultra-large deformation problems. The typical collapse patterns of granular columns are reproduced in the PFEM simulation and the physical mechanism behind the collapse phenomenon is provided. The collapse processes obtained from the PFEM simulation are compared to experimental observations and discrete element modeling, where a satisfactory agreement is achieved. The effects of the macro density and friction angle of the granular matter, as well as the roughness of the wall surfaces on the quasi-static collapse, are also investigated in this paper. Furthermore, our simulations reveal new quasi-static collapse patterns, as supplements to the ones already observed in the experimental tests, due to the change of the roughness of the basal surface.

Onset of structural evolution in granular materials as a redundancy problem

Abstract: The present paper is concerned with the redundancy of equations describing the static equilibrium of a granular assembly in relation to emergent behavioural features in granular materials such as critical state, jamming transition, instabilities and yielding It is proposed to link the concept of jamming to critical state phenomena by introducing a limiting micromechanical state at which large plastic (dissipative) structural evolution can occur, while static equilibrium is still maintained Such a state, herein coined as a Stable Evolution State (SES), can be numerically determined based on a number of 2D Discrete Element Method (DEM) simulations on loose granular assemblies for a given interparticle friction, but with varying contact stiffnesses, and subjected to various loading paths By tracing the evolutions of essential micro-variables such as fabric (contact normal) anisotropy, coordination number and rigidity ratio (ratio of mean contact force to contact stiffness and diameter) as well as the onset of plastic dissipation, a well-defined limit surface emerges in the space spanning coordination number, fabric anisotropy and rigidity ratio Interestingly, the same surface is reached when conducting other DEM simulations on dense granular assemblies with the same interparticle friction along a variety of loading paths and control conditions, thereby verifying the existence of such a characteristic SES surface This suggests a new reference state in granular materials which facilitates the mathematical formulation of multiscale constitutive laws as it provides an essential link to plastic yielding and critical state in geomaterials

Mesoscale simulation of clay aggregate formation and mechanical properties

Abstract: This paper proposes a novel methodology for understanding the meso-scale aggregation of clay platelets in water. We use Molecular Dynamics simulations using the CLAYFF force fields to represent the interactions between two layers of Wyoming montmorillonite (Na-smectite) in bulk water. The analyses are used to establish the potential of mean force at different spacings between the layers for edge-to-edge and face-to-face interactions. This is accomplished by finding the change in free energy as a function of the separation distance between the platelets using thermodynamic perturbation theory with a simple overlap sampling method. These nanoscale results are then used to calibrate the Gay–Berne (GB) potential that represents each platelet as a single-site ellipsoidal body. A coarse-graining upscaling approach then uses the GB potentials and molecular dynamics to represent the meso-scale aggregation of clay platelets (at submicron length scale). Results from meso-scale simulations obtain the equilibrium/jamming configurations for mono-disperse clay platelets. The results show aggregation for a range of clay platelets dimensions and pressures with mean stack size ranging from 3 to 8 platelets. The particle assemblies become more ordered and exhibit more pronounced elastic anisotropy at higher confining pressures. The results are in good agreement with previously measured nano-indentation moduli over a wide range of clay packing densities.

Packings of 3D stars: stability and structure

Abstract: We describe a series of experiments involving the creation of cylindrical packings of star-shaped particles, and an exploration of the stability of these packings. The stars cover a broad range of arm sizes and frictional properties. We carried out three different kinds of experiments, all of which involve columns that are prepared by raining star particles one-by-one into hollow cylinders. As an additional part of the protocol, we sometimes vibrated the column before removing the confining cylinder. We rate stability in terms of r, the ratio of the mass of particles that fall off a pile when it collapsed, to the total particle mass. The first experiment involved the intrinsic stability of the column when the confining cylinder was removed. The second kind of experiment involved adding a uniform load to the top of the column, and then determining the collapse properties. A third experiment involved testing stability to tipping of the piles. We find a stability diagram relating the pile height, h, versus pile diameter, $$\delta $$ , where the stable and unstable regimes are separated by a boundary that is roughly a power-law in h versus $$\delta $$ with an exponent that is less than unity. Increasing vibration and friction, particularly the latter, both tend to stabilize piles, while increasing particle size can destabilize the system under certain conditions.

The contact properties of naturally occurring geologic materials: experimental observations

Abstract: The discrete element method (DEM) is seeing widespread use in geotechnical applications and it is generally acknowledged that the validity of DEM simulations involving this class of materials depends critically on employing realistic contact laws. To support the development of such contact laws for common naturally occurring materials, we have conducted grain-to-grain contact experiments on several quartz sands, magnesite (limestone), crushed and ball-milled gneiss and ooids (precipitated calcium carbonate spheroids) and two reference materials (glass beads and the synthetic Delrin). Here we present the results of normal and shear contact experiments on these materials, with emphasis on the range of behavior encountered and aspects of behavior that deviate from current thinking on the topic. The development of contact laws based on the results presented herein, macroscopic frictional sliding and the implementation of the contact laws in DEM simulations are addressed in separate publications. The present experiments primarily examined the cyclic loading response, which allowed for a precise determination of normal and shear contact stiffness and loss compliances. Deformation generally consisted of elastic, anelastic and permanent components and the latter could be observed in shear prior to macroscopic sliding. Normal and shear stiffness ranged from 0.2–2.0 to 0.1– $$1.0\,\hbox {MN\,m}^{-1}$$ , respectively although the ratio of shear to normal stiffness for specific materials varied from 0.3 to $${\approx }1$$ . Frictional loss was observed to varying degrees in all of the contacts examined and internal friction in shear was found to be constant prior to the onset of permanent deformation. Internal friction ranged from barely perceptible to 0.1 for normal contacts and from 0.02 to 0.3 in shear. The modeling implications of the findings are examined as well.

Shear band formation in lunar regolith by discrete element analyses

Abstract: Few studies in shear band formation have considered the environmental conditions on the Moon, which however are significant for lunar regolith failure in future lunar exploration activities. This paper presents a numerical investigation into the mechanical behavior and strain localization of lunar regolith by means of the discrete element method (DEM). A micromechanical contact model for lunar regolith accounting for van der Waals forces and rolling resistance has been developed, then implemented into a DEM code, PFC2D, and finally applied to analyze the strain localization of lunar regolith through biaxial tests. Biaxial tests without considering van der Waals force effect were also performed as reference to compare with. The distributions inside the sample of grid deformation, void ratio, velocity, averaged pure rotation rate (APR), force chains and local stress during shear banding are analyzed. The simulations show that persistent bands are differently formed under Moon and Earth conditions. Van der Waals forces and rolling resistance play crucial roles in choosing persistent bands from various transient micro-bands before the peak state. Van der Waals forces lead to increased dilation and particle rotation, and enlarged “meso-voids” in force chain distributions within the persistent shear bands. The thickness (inclination to the horizontal) of shear band for the regolith under Moon condition is smaller (larger) than that for regolith under Earth condition.The fields of velocity and APR can reveal the finest heterogeneity in particle displacement (translation and rotation) in the form of transient micro-bands even at the very beginning of shear.

Shear strength of unsaturated granular soils: three-dimensional discrete element analyses

Abstract: To investigate the shear strength behavior of unsaturated granular soils, the three-dimensional discrete element method has been used to model soils in triaxial compression tests. A simple but effective contact model with an attractive capillary force was implemented. The effects of matric suction and packing density on shear strength of unsaturated granular assemblies were examined. The Mohr–Coulomb strength parameters (apparent cohesion and friction angle) were fitted for each matric suction examined. The results show that matric suction can increase the strength and modulus of granular soils and lead to increased dilation. The peak friction angle depends on the packing density but seems independent of matric suction. The apparent cohesion increases with matric suction non-linearly at a decreasing rate. Similar values of cohesion were observed for both dense and loose assemblies, which can be explained by the anisotropic distribution of capillary force network. Based on the microscopic observations, the stress-induced anisotropy of contact distributions leads to an anisotropic distribution of capillary water and, as a consequence, the capillary stress is anisotropic, imposing a shear effect on an assembly in parallel with that imposed by the externally applied loading. Consequently, the strength of unsaturated granular soil is controlled by the combined effects of packing density, and the magnitude and degree of anisotropy of the capillary stress. A new shear strength function for unsaturated soils, considering the anisotropic effects of matric suction, is proposed and validated using experimental data in the literature.

Analysis of the velocity field of granular hopper flow

Abstract: We report the analysis of radial characteristics of the flow of granular material through a conical hopper. The discharge is simulated for various orifice sizes and hopper opening angles. Velocity profiles are measured along two radial lines from the hopper cone vertex: along the main axis of the cone and along its wall. An approximate power law dependence on the distance from the orifice is observed for both profiles, although differences between them can be noted. In order to quantify these differences, we propose a Local Mass Flow Index that is a promising tool in the direction of a more reliable classification of the flow regimes in hoppers.

Using PIV to measure granular temperature in saturated unsteady polydisperse granular flows

Abstract: The motion of debris flows, gravity-driven fast moving mixtures of rock, soil and water can be interpreted using the theories developed to describe the shearing motion of highly concentrated granular fluid flows. Frictional, collisional and viscous stress transfer between particles and fluid characterizes the mechanics of debris flows. To quantify the influence of collisional stress transfer, kinetic models have been proposed. Collisions among particles result in random fluctuations in their velocity that can be represented by their granular temperature, T. In this paper particle image velocimetry, PIV, is used to measure the instantaneous velocity field found internally to a physical model of an unsteady debris flow created by using “transparent soil”—i.e. a mixture of graded glass particles and a refractively matched fluid. The ensemble possesses bulk properties similar to that of real soil-pore fluid mixtures, but has the advantage of giving optical access to the interior of the flow by use of plane laser induced fluorescence, PLIF. The relationship between PIV patch size and particle size distribution for the front and tail of the flows is examined in order to assess their influences on the measured granular temperature of the system. We find that while PIV can be used to ascertain values of granular temperature in dense granular flows, due to increasing spatial correlation with widening gradation, a technique proposed to infer the true granular temperature may be limited to flows of relatively uniform particle size or large bulk.