Discrete element modelling of two-layered ballast in a box test

It has been recently reported that ballast comprising differently graded layers helps to reduce track settlement. The main goal of this paper is to provide micro mechanical insight about how the differently layered ballasts reduce the settlement by employing DEM and thus propose an optimum design for two-layered ballast. The DEM simulations provide sufficient evidence that the two-layered ballast works by preventing particles from moving laterally through interlocking of the particles at the interface of the different layers in a similar way to geogrid. By plotting the lateral force acting on the side boundary as a function of the distance to the base, it is found that the walls in the region of 60-180 mm above the base alway support the largest lateral forces and therefore this region might be the best location for an interface layer. However, considering the weak improvement in performance by increasing the thickness of the layer of scaled (small) ballast from 100 mm to 200 mm, it is suggested that it is best to use the sample comprising 100 mm scaled ballast on top of 200 mm standard ballast as the most cost effective solution

Micro mechanics of the critical state line at high stresses

A critical state line is presented for a crushable numerical soil, which is parallel to the isotropic normal compression line. A previous theory for the normal compression line, which correctly predicts the slope as a function of the size-effect on particle strength is extended to justify the slope of the critical state line. The micro mechanics behind critical states are examined, leading to a theory for a relationship between the volume of smallest particles and mean effective stress. A unique relationship exists for crushed states, leading to a two-dimensional interpretation of the state boundary surface for soils looser than critical

Micro mechanics of drained and undrained shearing of compacted and overconsolidated crushable sand

A numerical crushable soil sample has been created using the previously published McDowell and de Bono (2013) model and subjected to a range of stress paths. Compacted sand simulations are performed using conventional triaxial stress paths, constant mean stress and constant volume conditions and a critical state line established. Overconsolidated samples have been created by crushing the soil down the isotropic normal compression line, unloading, and shearing at constant radial stress, constant mean stress or constant volume and a critical state line is again established. The critical state line is unique at high stresses for the simulated compacted and overconsolidated sands and is parallel to the isotropic normal compression line, in agreement with available data and a previously published theory. The critical state line at low stress levels is non-unique and a function of the particle size distribution, in agreement with available data. Constant volume tests exhibit the well-known phenomena of phase transformation points and peak strengths are observed for ‘drained’ soils on the dense side of critical. The numerical soil produces a state boundary surface that compares well to available data

On the packing and crushing of granular materials

This paper is a study of the dependence of the volume of voids in a granular material on the particle size distribution. It has previously been proposed that the volume of voids is proportional to the volume of the smallest particles. In a particle size distribution which is progressively becoming wider (e.g. as occurs due to crushing during the compression of sand), the smallest size of particle decreases, yet there are only ever a few of these particles out of many thousands or millions. This paper attempts to identify which particles govern the overall density of a granular material, and a new definition of the ‘smallest particles’ is proposed. These particles are shown to govern the void space in a range of simulations of spherical and non-spherical crushable particles. The theory also applies to idealised Apollonian sphere packings

The fractal micro mechanics of normal compression

The fundamental fractal micro mechanics of normal compression of granular materials is studied using DEM. This paper examines the emergence of a finite fractal bounded by two particle sizes as stress increases, and the evolution of various definitions of the ‘smallest particles’. It is revealed that if particles are categorised according to their coordination number, then the volume of all particles with 4 contacts or fewer is directly proportional to the void space. These particles are called ‘critical particles’ and are shown, for the first time, to explain quantitatively the voids reduction with increasing vertical stress

Discrete element modelling of a flexible membrane for triaxial testing of granular material at high pressures

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

Modelling real particle shape in DEM: a comparison of two methods with application to railway ballast

Two different methods for the modelling of real particle shape in 3D DEM simulations are assessed in this paper. The first method uses overlapping spheres (clumps), while the second uses a block defined as a closed and convex polyhedron. The two methods are applied to the modelling of triaxial tests on a railway ballast. The macroscopic responses obtained with the two methods are compared, and it is observed that with clumps a higher shear strength, closer to the experimental response, can generally be achieved. A micromechanical analysis is also carried out to highlight how the modelled particle shape affects the mechanics, and consequently explain the difference in the macroscopic response. It is observed, in particular, that a key feature of real particle shape is concavity, that plays an important role in the mechanics of a granular assembly. Finally, the combined effect of particle shape and interparticle friction coefficient on the shear strength is assessed. This confirms that even for real (angular) shapes, peak strength increases with interparticle friction, while critical state strength first increases and then tends to saturate above a certain interparticle friction

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

Waveform-based simulated annealing of crosshole transmission data: a semi-global method for estimating seismic anisotropy

We successfully apply the semi-global inverse method of simulated annealing to determine the best-fitting 1-D anisotropy model for use in acoustic frequency domain waveform tomography. Our forward problem is based on a numerical solution of the frequency domain acoustic wave equation, and we minimize wavefield phase residuals through random perturbations to a 1-D vertically varying anisotropy profile. Both real and synthetic examples are presented in order to demonstrate and validate the approach. For the real data example, we processed and inverted a cross-borehole data set acquired by Vale Technology Development (Canada) Ltd. in the Eastern Deeps deposit, located in Voisey's Bay, Labrador, Canada. The inversion workflow comprises the full suite of acquisition, data processing, starting model building through traveltime tomography, simulated annealing and finally waveform tomography. Waveform tomography is a high resolution method that requires an accurate starting model. A cycle-skipping issue observed in our initial starting model was hypothesized to be due to an erroneous anisotropy model from traveltime tomography. This motivated the use of simulated annealing as a semi-global method for anisotropy estimation. We initially tested the simulated annealing approach on a synthetic data set based on the Voisey's Bay environment; these tests were successful and led to the application of the simulated annealing approach to the real data set. Similar behaviour was observed in the anisotropy models obtained through traveltime tomography in both the real and synthetic data sets, where simulated annealing produced an anisotropy model which solved the cycle-skipping issue. In the real data example, simulated annealing led to a final model that compares well with the velocities independently estimated from borehole logs. By comparing the calculated ray paths and wave paths, we attributed the failure of anisotropic traveltime tomography to the breakdown of the ray-theoretical approximation in the vicinity of strong velocity discontinuitie

Relating Hydraulic Conductivity to Particle Size Using DEM

For over 100 years it has been accepted that the permeability or hydraulic conductivity of a soil is controlled by the size of pores through which the fluid flows, and that this pore size should be a function of particle sizes. All well-known formulas (such as the empirical Hazen or analytical Kozeny–Carman) are based on the squared value of some characteristic particle or pore size. Recent work has established which particles control the porosity or density of a granular material, so it follows that these particles may also govern the hydraulic conductivity. In this work, a new yet simple technique was used to obtain a characteristic “smallest” particle size, which is a function of both the particle size distribution and the geometrical packing. The use of this new proposed characteristic particle size was shown to be valid both theoretically and in comparison with the characteristic particle or pore sizes used in classical predictive methods for the permeability of granular materials. A very simple fractal theory showed what the characteristic particle size that controls conductivity should be, and a simple discrete element simulation was used to confirm the result