Discrete-element modelling has been used to investigate the micro mechanics of one-dimensional compression. One-dimensional compression is modelled in three dimensions using an oedometer and a large number of particles, and without the use of agglomerates. The fracture of a particle is governed by the octahedral shear stress within the particle due to the multiple contacts and a Weibull distribution of strengths. Different fracture mechanisms are considered, and the influence of the distribution of fragments produced for each fracture on the global particle size distribution and the slope of the normal compression line is investigated. Using the discrete-element method, compression is related to the evolution of a fractal distribution of particles. The compression index is found to be solely a function of the strengths of the particles as a function of size.

Previous work by the authors using the discrete-element method (DEM) has used the octahedral shear stress within a sphere together with a Weibull distribution of strengths and a size effect on average strength, to determine whether fracture occurs or not. This leads to fractal particle size distributions and a normal compression line which are consistent with experimental data. However, there is no agreement in the literature as to what the fracture criterion should be, and as yet it is not clear whether other criteria could lead to the correct evolution of voids ratio and particle size distribution under increasing stress. Various possibilities for the criterion have been studied in detail here to ascertain whether these other criteria may give the correct behaviour under normal compression. The use of the major principal stress within a particle, the mean stress and the stress calculated from the maximum contact force on a particle are each investigated as alternatives to the octahedral shear stress. Only the criterion based on the maximum contact force is shown to give behaviour observed experimentally and the simulations shed further insight into the micro mechanics of normal compression.

This paper presents simulations of high-pressure triaxial shear tests on a crushable sand. The discrete element method is used, featuring a large number of particles and avoiding the use of agglomerates. The triaxial model features a flexible membrane, therefore allowing realistic deformation, and a simple breakage mechanism is implemented using the octahedral shear stress induced in the particles. The simulations show that particle crushing is essential to replicate the realistic behaviour of sand (in particular the volumetric contraction) in high-pressure shear tests. The general effects of crushing during shear are explored, including its effects on critical states, and the influence of particle strength and confining pressure on the degree of crushing are discussed.

Discrete element modelling has been used to investigate the micro mechanics of isotropic normal compression. One-dimensional (1D) normal compression has previously been modelled in three dimensions using an oedometer and a large number of particles and without the use of agglomerates, and it was shown that the compression index was solely related to the strengths of the particles as a function of size. The same procedure is used here to model isotropic normal compression. The fracture of a particle is governed by the octahedral shear stress within the particle (due to the multiple contacts) and a Weibull distribution of strengths. The octahedral shear stresses, due to local anisotropic stresses within a sample with isotropic boundary stresses, are shown to give rise to a normal compression line (NCL) and the evolution of a distribution of particle sizes. The compression line is parallel to the 1D NCL in log e-log p space, in agreement with traditional critical state soil mechanics and confirming that the compression index is solely a function of the size effect on average particle strength, which determines the hardening law for the material. The paper shows, for the first time, how local octahedral shear stresses induced in the particles within the sample generate an isotropic normal (clastic) compression line.

Dariusz (2012) Discrete element modelling of a flexible membrane for triaxial testing of granular material at high pressures. Géotechnique Letters, 2 (4). pp. 199-203. ISSN 2045pp. 199-203. ISSN -2543 Access from the University of Nottingham repository: http://eprints.nottingham.ac.uk/3286/1/de_Bono_et_al._ %282012%29_Triaxial_Membrane.pdf Copyright and reuse:The Nottingham ePrints service makes this work by researchers of the University of Nottingham available open access under the following conditions. This article is made available under the University of Nottingham End User licence and may be reused according to the conditions of the licence. For more details see: http://eprints.nottingham.ac.uk/end_user_agreement.pdf A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. The discrete element method (DEM) has been used to simulate triaxial tests on a bonded material at high pressures. A key feature of the model is the use of a flexible membrane that allows the correct volumetric deformation and the true failure mode to develop while applying constant confining pressure to the triaxial sample. The correct pattern of behaviour has been observed across a wide range of confining pressures, with both shear planes and barrelling failure being observed. The radial pressure applied by the membrane remains constant after large strains and deformation.

It has recently been shown that the onedimensional normal compression of sand can be modelled effectively in three-dimensions using the discrete element method, and that the slope of the compression curve (in log voids ratio-log stress space) is controlled by the size effect on average particle strength. This paper incorporates soil structure by simulating cemented sand, and the effects of interparticle bonding (including bond strength and strength distributions) on the one-dimensional compression behaviour and evolving particle size distributions are investigated. The results show that bonding reduces particle crushing, and it is both the magnitude and distribution of bond strengths that influence the compression curve of the structured material.

The micro mechanics of one-dimensional and isotropic normal compression of granular soil have recently been revealed using the discrete element method. By modelling soil grains as spheres and implementing a new crushing model, the authors have previously investigated the influence of fracture mechanism, particle strengths (and distributions), and the size-hardening law on both the normal compression line and resultant particle size distribution; this resulted in a new compression law. In this work, irregular particle shape is introduced, using 'clumps' (groups of spherical particles), allowing different relative densities of the same material to be subjected to normal compression. An investigation into the mechanics of yielding is presented, in which the onset of crushing is related to the average particle octahedral shear stress and 'yield' is seen to be a function of the available void space. Beyond yield, the normal compression lines for the clumps at different initial densities are examined and compared to that for spheres. The effect of coordination number and particle shape on the normal compression are studied, and in particular the micro mechanics behind the evolution of a fractal particle size distribution are revealed.

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