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Particle breakage is of fundamental importance for understanding the mechanical behaviour of sands and is relevant to many geotechnical engineering problems. In order to gain new insights into the mechanism of breakage of individual sand particles under single-particle compression, this study combines mechanical tests with three-dimensional X-ray micro-computed tomography (μCT) performed 'in situ', that is, during loading. A novel mini-loading apparatus was developed to perform in-situ compression tests within a laboratory nanofocus X-ray CT. The tests were performed on eight particles, four Leighton Buzzard sand (LBS) particles and four highly decomposed granite (HDG) particles, to study their different fracture mechanisms. A series of image processing and analysing techniques was utilised to obtain both qualitative and quantitative results. The most important factors in determining the fracture patterns of the LBS and HDG particles were found to be particle morphology and initial microstructure, respectively. Versatile fracture patterns deviating from simple vertical splitting were observed, particularly in HDG particles. The change of morphology parameters during loading was found to depend on the fracture mechanisms and material properties, independently of their initial values. The fragments of both the LBS and HDG particles satisfy the fractal distribution, which indicates that the fragmentation is scale invariant. Different energy dissipation mechanisms were found. The energy dissipation by friction gradually prevails against the energy dissipated in generating new surfaces.

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SUMMARYA discrete element modelling of naturally microstructured sands is very important to geomechanics. This paper presents a simple discrete element model for naturally microstructured sands with the aim to efficiently capture the effect of cementation between particles (bonds). First, a simple bond contact model was proposed by introducing a rigid-plastic bond element into the conventional contact model for dry granular material. Second, efficient numerical techniques were investigated to implement this contact model into the distinct element method (DEM). Then, a two-dimensional DEM code was developed to simulate a series of isotropic compression tests on the materials of different densities and bonding strengths. The study shows that the DEM model is able to capture the main features of naturally microstructured sands, such as variations of yielding and bulk modulus against bonding strength or material density. In addition, it is shown that the gross yielding (the yielding defined in terms of strains) is largely related to bond breakage; Coop and Willson criteria are generally reasonable; and the strong bonding in the experimental data obtained by Rotta et al. comes from that their bonded materials start at different points on the same compression line.

SUMMARYThe purpose of this paper is to present a physically based plasticity model for non-coaxial granular materials. The model, which we shall call the double slip and rotation rate model (DSR 2 model), is a pair of kinematic equations governing the velocity field. The model is based on a discrete micro-analysis of the kinematics of particles in contact, and is formulated by introducing a quantity called the averaged micropure rotation rate (APR) into the unified plasticity model which was proposed by one of the authors. Our macro-micro mechanical analysis shows that the APR is a non-linear function of, among other quantities, the macro-rotation rate of the major principal axis of stress taken in the opposite sense. The requirement of energy dissipation used in the double-sliding free-rotating model appears to be unduly restrictive as a constitutive assumption in continuum models. In the DSR 2 model the APR tensor and the spin tensor are directly linked with non-coaxiality of the stress and deformation rate tensors. We also propose a simplified plasticity model based on the DSR 2 model for a class of dilatant materials, and analyse its material stability.

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