This paper describes an experimental study examining the influence of the mechanical and geometrical properties of the constituent grains on the overall material response of cohesionless granular materials. Glass ballotini were used as an analogue soil; their relatively simple geometry allowed the influence of particle shape and inter-particle friction to be examined independently. Techniques were developed to control the surface roughness of the ballotini to facilitate a parametric study. The particle shape was also varied by crushing the ballotini. At the micro-scale, the particle characterisation included accurate measurements of inter-particle friction, contact stiffness, particle surface roughness and particle shape. At the macro-scale the sensitivity of overall material response to changes in surface roughness and geometry was characterised using triaxial tests and oedometer tests on smooth spherical ballotini, roughened ballotini and crushed angular ballotini. Compression tests indicated that the initial load deformation response at particle–particle contact points is significantly softer than previously believed. Optical interferometry of particles after single particle–particle shearing tests confirmed that plastic strains occurred at the contact point, which were related to plastic yield. A Hertzian response was only seen at higher contact loads. A clear relationship between the inter-particle friction and the particle surface roughness was found. However, the macro-scale experiments indicated that while the material response may be slightly dependent on the surface roughness and friction, the influence of particle shape is very much more significant.

The distinct element method as proposed by Cundall and Strack uses the computationally efficient, explicit, central difference time integration scheme. A limitation of this scheme is that it is only conditionally stable, so small time steps must be used. Some researchers have proposed using an implicit time integration scheme to avoid the stability issues arising from the explicit time integrator typically used in these simulations. However, these schemes are computationally expensive and can require a significant number of iterations to form the stiffness matrix that is compatible with the contact state at the end of each time step. In this paper, a new, simple approach for calculating the critical time increment in explicit discrete element simulations is proposed. Using this approach, it is shown that the critical time increment is a function of the current contact conditions. Considering both two-and three-dimensional scenarios, the proposed refined estimates of the critical time step indicate that the earlier recommendations contained in the literature can be unconservative, in that they often overestimate the actual critical time step. A three-dimensional simulation of a problem with a known analytical solution illustrates the potential for erroneous results to be obtained from discrete element simulations, if the time-increment exceeds the critical time step for stable analysis.

Over the past 50 years, experimental studies have repeatedly demonstrated that the mechanical behaviour of sand is sensitive to the material fabric, that is, the arrangement of the grains. Up until now there have been relatively few attempts to describe this fabric quantitatively. Much of our understanding of the link between the particle movements and interactions and the macro-scale response of granular materials, including sand, comes from discrete-element modelling and experiments on 'analogue' sands with simple, idealised shapes. This paper investigates methods of quantifying the directional fabric of a real sand and its evolution under loading. Statistical analyses of the distribution of fabric directional data in terms of particle, contact normal, branch vector and void orientations were carried out at different stages of shearing deformation. The data show that the initial particle orientation fabric that develops during the deposition of the material tends to persist during shearing, while in the post-peak regime the contact normals seem to be reoriented along the direction of the major principal stress. Different patterns were observed within the shear band, as both the particles and the contact normal vectors appeared to rotate along the shear plane.

SUMMARY Understanding the extent to which discrete element method (DEM) simulations can capture the critical state characteristics of granular materials is important to legitimize the use of DEM in geomechanics. This paper documents a DEM study that considered the sensitivity of the critical state response characteristics to the coefficient of interparticle friction (μ) using samples with gradings that are representative of a real soil. Most of the features that are typically associated with sand behaviour at the critical state were seen to emerge from the DEM simulation data. An important deviation occurs when high μ values (μ  ≥ 0.5) are used, as has been the case in a number of prior DEM studies. While there is a systematic variation in the critical state behaviour with μ for μ  < 0.5, when μ ≥ 0.5, the behaviour at the critical state seems to be insensitive to further increases in μ. In contrast to observations of conventional soil response, when μ ≥ 0.5, the void ratio at the critical state initially increases with increasing mean effective stress (p′). Analysis of the DEM data and use of simple models of isolated force chains enabled some key observations. When ‘floating’ particles that do not transmit stress are eliminated from the void ratio calculation, the void ratio at the critical state decreases consistently with increasing p′. There is a transition from sliding to rolling behaviour at the contact points as μ increases. Beyond a limiting value of μ, further increases in μ do not increase the buckling resistance of individual strong force chains. Copyright © 2014 John Wiley & Sons, Ltd.

The triaxial test is probably the most important fundamental laboratory test for geotechnical engineers. The objective of the study presented here was to gain insight into the micro-scale interactions experienced by particles during a triaxial test using the distinct element method (DEM). To achieve this objective, a novel DEM modelling environment to simulate triaxial tests on ideal granular materials was implemented, as described here. In this test environment, both the stress conditions and boundary conditions in the physical tests can be accurately reproduced. This approach was quantitatively validated by simulating a number of physical triaxial tests on specimens of steel spheres. A comparison between the circumferential periodic boundaries used here and the circumferential rigid boundaries used by other researchers emphasises the significance of maintaining a continuous particle-particle contact network orthogonal to the major principal stress direction.Results of an analysis of the micro-scale response in a triaxial simulation are analysed in detail, including the stresses, the distribution of contact forces, the evolution of fabric, the distribution of local strains, and the particle rotations. Significant non-uniformities in the stresses, strains and contact fabric were observed.

SUMMARYDiscrete element modelling is a viable alternative to conventional continuum-based analysis for analysing problems involving localized deformations of particulate media. However, to aid in the interpretation of the results, it is useful to express the results of discrete element analyses in terms of the continuum parameters of stress and strain. A number of homogenization methods have been proposed to calculate strain in discrete systems; however, two significant limitations of these methods remain. First, none of these methods incorporate particle rotation effects satisfactorily, although significant particle rotation occurs in shear bands in both physical tests and numerical simulations of granular materials. Additionally, observations of the particle displacement fields in shear bands in granular materials indicate that the displacements within the localizations are erratic. Consequently, existing linear, local interpolation approaches produce substantial variations in the strain values calculated in adjacent elements in the region of localization, hindering clear visualization of the strain localization as it evolves. A new method of domain discretization for calculating strain is proposed. This method is capable of capturing particle rotation and employs a non-local meshfree interpolation procedure capable of smoothing the erratic displacements in strain localizations, which better defines their evolution. The proposed method is validated for problems involving both two and three dimensions. A number of methods are compared with the proposed method and pertinent insights are made.

Dynamic loading of embankment, foundation and pavement structures results in particle breakage of the constituent granular materials, when the stresses imposed on their particles exceed their strength. This paper presents the results of a number of drained cyclic triaxial tests on loose, uniformly graded samples of Dogs bay carbonate sand. It is observed that particle breakage is dependent on stress level, cyclic stress ratio, and creep and is directly related to volumetric strain. Drained cycling increases volumetric strain and therefore more breakage occurs when larger numbers of cycles are imposed. The increase in particle breakage from one cycle to the next indicates that while particles may not be loaded to their full capacity in a given cycle, they can be crushed in subsequent cycles without any variation in the amplitude of cyclic loading.

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