On the micro mechanics of one-dimensional normal compression

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

A new creep law for crushable aggregates

The authors have recently proposed a new equation for the one-dimensional (1D) normal compression line, which contains a parameter controlling the size effect on average strength. They showed that the equation held for a wide range of discrete-element modelling (DEM) simulations of crushable aggregates. This paper incorporates the time-dependence of particle strength. A new equation is proposed and examined using DEM of 1D creep. The simulations show that while the plots may seem linear on a plot of voids ratio against the logarithm of time in the traditional way, the new proposed law, which is linear when the voids ratio is also plotted on a logarithmic scale, is more appropriate. The simulations examine the influence of the size effect hardening law, the time dependence on strength and stress level. It is shown that the new equation holds for each case

Particle breakage criteria in discrete-element modelling

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

Discrete element modelling of creep of asphalt mixtures

Creep tests on asphalt mixtures have been undertaken under four stress levels in the laboratory while the Discrete Element Model (DEM) has been used to simulate the laboratory tests. A modified Burger’s model has been used to represent the time-dependent behaviour of an asphalt mixture by adding time-dependent moment and torsional resistance at contacts. Parameters were chosen to give the correct stress-strain response for constant strain rate tests in Cai et al. (2013) . The stress-strain response for the laboratory creep tests and the simulations were recorded. The DEM results show reasonable agreement with the experiments. The creep simulation results proved to be dependent on both bond strength variability and positions of the particles. Bond breakage was recorded during the simulations and used to investigate the micro-mechanical deformation behaviour of the asphalt mixtures. An approach based on dimensional analysis is also presented in this paper to reduce the computational time during the creep simulation, and this analysis is also a new contribution

Discrete element modelling of rock communition in a cone crusher using a bonded particle model

It is known that discrete element method modelling (DEM) of rock size reduction can be achieved by two approaches: the population balance model (PBM) and the bonded particle model (BPM). However, only PBM has been successfully used in DEM modelling cone crusher in the literature. The aim of this paper is to explore the feasibility of using the BPM to represent the size reduction of rock experienced within the cone crusher chamber. The feed rock particles were represented by isotropic dense random packing agglomerates. The simulation results were compared with the PBM simulation results, and it was shown that the BPM cone crusher model was able to satisfactorily replicate the performance of a cone crusher as well and it can provide more accurate prediction of the percentage of the fine products. In addition, the novel contribution here is that the rock feed material comprises particles of realistic shapes which break into more realistically shaped fragments compared with the fragments with defined shapes in the PBM model

Energy dissipation in soil samples during drained triaxial shearing

The discrete-element method was used to simulate drained triaxial compression of large-scale, polydisperse numerical samples at a range of void ratios while tracing all relevant energy components. The frictional dissipation and boundary work are almost equal regardless of sample density. The volumetric work reaches a steady value at large strain. However, the distortional work increases continually as sample deformation continues post-critical state. There is a preferential orientation for frictional dissipation at around 45° to the major principal stress direction. This matches the orientation at which there is the largest number of sliding contacts. The work equations, which are fundamental in most commonly used constitutive models, are linear when plotted against deviatoric strain. The modified Cam Clay work equation substantially over-predicts the frictional dissipation for dense samples. An alternative, thermodynamically consistent work equation gives a much better description of frictional dissipation and is therefore recommended to ensure accuracy in modelling

Prediction of strength and deformability of an interlocked blocky rock mass using UDEC

The accurate prediction of strength and deformability characteristics of a rock mass is very challenging. In practice, properties of a rock mass are often estimated from available empirical relationships based on the uniaxial compressive strength (UCS). However, UCS does not always give a good indication of in-situ rock mass strength and deformability. The aim of this paper is to present a methodology to predict the strength and deformability of a jointed rock mass using UDEC (universal distinct element code). In the study, the rock mass is modelled as an assemblage of deformable blocks that can yield as an intact material and/or slide along pre-defined joints within the rock mass. A range of numerical simulations of UCS and triaxial tests were conducted on rock mass samples in order to predict the equivalent mechanical properties for the rock mass under different loading directions. Results are compared against the deformability parameters obtained by analytical methods

Discrete element modelling of a rock cone crusher

The feasibility of the discrete element method to model the performance of a cone crusher comminution machine has been explored using the particle replacement method (PRM) to represent the size reduction of rocks experienced within a crusher chamber. In the application of the PRM method, the achievement of a critical octahedral shear stress induced in a particle was used to define the breakage criterion. The breakage criterion and the number and size of the post breakage progeny particles on the predicted failure of the parent particles were determined from the results of an analysis of the experimental data obtained from diametrical compression tests conducted on series of granite ballast particles. The effects of the closed size setting (CSS) and eccentric speed settings on the predicted product size distribution compare favourably with the available data in the literature

Numerical modelling of Non-Transform Discontinuity geometry: Implication for ridge structure, volcano-tectonic fabric development and hydrothermal activity at segment ends.

Ocean ridge discontinuities partition and offset spreading centres at a range of scales. Large scale discontinuities (10's–100's km) are synonymous with first-order transform faults, which have well defined linear fault zone valleys. In contrast, Non-Transform Discontinuities (NTDs) are diffuse, smaller scale offsets (0 to b20 km), characterised by central basins or topographic highs. The geometry of NTD offsets can be categorised by the sense of offset, either right-stepping or left-stepping, and by the relative positions of the segment tips. The segment tip configurations include under-lapping, over-lapping or simple across-axis jumps or stepping in the ridge axis. In this study finite difference software is used to model segment geometry at a slow-spreading ridge under a normal tensile-stress within a homogeneous and isotropic medium. Along- and across-axis segment separations were varied incrementally for left- and right-stepping senses. The results show that the ratio of along-axis to across-axis segment tip separation is a dominant control of stress field rotation within an NTD. Features which most clearly show rotation within an NTD include basins and tectonically controlled constructional ridges. The obliquity of these features along with measurements of the surrounding fault fabrics are used as a way of observing and determining stress rotations within NTDs along the Central Indian Ridge (CIR). These rotations were used to obtain segment geometries from models where the central tensor showed an equivalentrotation. The results show that geometry has a profound effect on stress field rotation under which large- and small-scale volcanotectonic fabrics form. In addition, a shortfall of the predicted model tip relative to interpreted positions, along with morphology and observation of the ridge fabrics at the terminations to some segments, suggests the existence of a zone, broadly analogous to theprocess zone observed in fracture mechanics, which we call a damage zone. Given the criteria for the promotion of hydrothermal circulation, this damage zone would have a greater potential for hosting hydrothermal activity.<br/