G. R. McDowell

The fractal crushing of granular materials

Abstract A study has been made of the micro mechanical origins of the irrecoverable compression of aggregates which comprise brittle grains. The terms “yielding” and “plastic hardening” are used in the discipline of soil mechanics to describe the post-elastic behaviour of granular media. These “plastic” phenomena are here related to the successive splitting of grains. Grains are taken to split probabilistically; the likelihood increasing with applied (macroscopic) stress; but reducing with any increase in the co-ordination number and with any reduction in particle size. When the effect of the co-ordination number dominates; a simple numerical model confirms published findings that a fractal distribution of particle sizes evolves from the compression of an aggregate of uniform grains. Taking the production of new surface area from the particle size distributions produced by the numerical model; a work equation is used to deduce the plastic compression of voids; for one-dimensional compression of the aggregate. This too is shown to be in agreement with experimental data; and in particular confirms the linearity of plots of voids ratio versus the logarithm of stress. The gradient of these plots is for the first time related to fundamental material parameters.

USE OF THE DISTINCT ELEMENT METHOD TO MODEL THE DEFORMATION BEHAVIOR OF AN IDEALIZED ASPHALT MIXTURE

This paper investigates the use of distinct element modelling to simulate the behavior of a highly idealized bituminous mixture in an uniaxial compressive creep test. The effect of bitumen is represented as shear and normal contact stiffnesses. Elastic contact properties have been used to investigate the effect of sample size and the effect of the values of the shear and normal contact stiffnesses on bulk material properties. It was found that a sample containing at least 4,500 particles is required for Youngs modulus and Poissons ratio to be within 2% of the values calculated using a much larger number of particles. The bulk modulus was found to be linearly dependent on the normal contact stiffness and independent of the shear contact stiffness. Poissons ratio was found to be dependent on only the ratio of the shear contact stiffness to the normal contact stiffness. A simple elasto-visco-plastic Burgers model was introduced to give time dependent shear and normal contact stiffnesses.

A simple method to create complex particle shapes for DEM

In order to get quantitatively reliable results with the discrete element method, or DEM, it becomes more and more necessary to reproduce accurately the shape of irregular particles. A simple and fast original method to create complex shapes by assembling spheres together is proposed. This paper shows its ability to reproduce a shape, its degree of resolution and the number of spheres required.

On the use of discrete element modelling to simulate the viscoelastic deformation behaviour of an idealized asphalt mixture

The use of discrete-element modelling (DEM) to simulate the behaviour of a highly idealized bituminous mixture under uniaxial and triaxial compressive creep tests is investigated in this paper. The idealized mixture comprises single-sized spherical particles (sand) mixed with bitumen and was chosen so that the packing characteristics are known and the behaviour of the mixture is dominated by the bitumen. The bitumen is represented as shear and normal (tensile and compressive) contact stiffnesses. Numerical sample preparation procedures for specimens containing spherical particles or clumps have been developed to ensure that the final specimen is isotropic and has the correct volumetric proportions. An elastic contact was used for the compressive normal contact stiffness and a viscoelastic contact was used for shear and tensile normal contact stiffness. Simulation results show that the idealized mixture is found to dilate when the ratio of compressive to tensile contact stiffness increases as a function of loading time. Uniaxial and triaxial viscoelastic simulations have been performed to investigate the effect of stress ratio on dilation and the numerical results have been verified with experimental data. The effects of introducing a proportion of frictional contacts and a more complex particle shape (clump) on dilation have been examined.

Discrete element modelling of railway ballast under triaxial conditions

Railway ballast is a granular material with a complex stress–strain relationship under monotonic loading. The discrete element method has been widely used to investigate the mechanical behaviour for the behaviour of granular materials. In this paper, discrete element modelling has been used to capture the essential mechanical features of railway ballast. The effects of particle shape and interparticle friction have been studied. Parallel bonds have also been introduced in the simulations to simulate the interlocking of small-scale asperities, so that the correct stress–strain relationship for ballast can be modelled. Asperity breakage has been modelled by using small balls bonded at the edges of the main body of a particle. A range of confining pressures have been applied to the assembly of particles. The simulations demonstrate the validity of numerical modelling of railway ballast. In particular, the unique contribution of this paper is to show that the monotonic shearing behaviour of railway ballast can be correctly modelled under a range of confining pressures, providing micromechanical insight into the behaviour.

Effect of particle size distribution on pile tip resistance in calcareous sand in the geotechnical centrifuge

Abstract Until recently, the micro mechanical origins of soil behaviour have remained illusive, but it is now known that that the constitutive behaviour of a soil is largely determined by its particle size distribution. This paper examines the specific boundary problem associated with the penetration of a model pile into two different gradings of dry calcareous sand in a geotechnical centrifuge, in order to establish the effect of the inclusion of fine particles on the pile end bearing resistance. The first grading of sand comprised particles smaller than 0.5 mm; the second grading contained particles of nominal size d such that 0.15 mm < d < 0.5 mm. Each test was performed on each of two samples of each grading. Tip resistance was observed to rise to a peak at shallow depths, and then fall; a micro mechanical explanation is presented for this instability. Following the centrifuge tests, particles were retrieved from the centres of the soil samples, where the pile had previously been driven, for subsequent particle size analysis. It was found that insignificant crushing had occurred in the sand retrieved from depths less than the depth of peak resistance, but that significant crushing had occurred in the sand retrieved from greater depths. The peak in tip resistance was a factor of two larger for the well-graded sand, but the ultimate tip resistance at greater depths was found to be approximately independent of the initial particle size distribution for all four tests. A micro mechanical explanation is also proposed for this observation.

Discrete Element Modeling of Constant Strain Rate Compression Tests on Idealized Asphalt Mixture

Discrete element modeling has been used to simulate constant strain rate compressive tests for an idealized asphalt mixture comprising approximately single-sized sand particles. A range of constant strain-rate compressive tests to failure have been undertaken in the laboratory and the axial stress-strain response has been carefully measured. The peak stress (compressive strength) of the material was found to be as a power-law function of the equivalent (temperature compensated) strain rate in the viscoelastic region of behavior. The internal geometry of the idealized asphalt mixture has been reproduced in PFC-3D and internal damage (cracking) in the material was modeled by allowing bond breakage between adjacent particles. Elastic contact properties have been used to investigate the effect of random variations in internal sample geometry, the distribution of bond strengths between adjacent particles and the coefficient of friction between particles where the bond has broken. A simple viscoelastic Burgers model was used to introduce time dependent shear and normal (tensile) contact stiffnesses and an elastic contact has been assumed for the compressive normal contact stiffness. To reduce the computation time, both viscosities in the Burgers model were scaled which has been shown to have the same effect as scaling the loading velocity (strain rate) by the same factor. A strain rate dependent bond breakage criterion has been developed and model results were found to compare well with the experimental data.

A study of geogrid-reinforced ballast using laboratory pull-out tests and discrete element modelling

This paper presents an evaluation of the behaviour of geogrid-reinforced railway ballast. Experimental large box pull-out tests were conducted to examine the key parameters influencing the interaction between ballast and the geogrid. The experimental results demonstrated that the triaxial geogrid outperforms the biaxial geogrid and the geogrid aperture size is more influential than rib profile and junction profile. The discrete element method (DEM) has then been used to model the interaction between ballast and geogrid by simulating large box pull-out tests and comparing with experimental results. The DEM simulation results have been shown to provide good predictions of the pull-out resistance and reveal the distribution of contact forces in the geogrid-reinforced ballast system. Therefore, the calibrated geogrid model and the use of clumps to model ballast particles hold much promise for investigating the interaction between geogrids and ballast and therefore optimising performance.

Discrete Element Modeling of Cone Penetration Tests Incorporating Particle Shape and Crushing

AbstractThe effect of particle shape and particle crushing on the results of cone penetration testing (CPT) of granular materials in a calibration chamber has been studied using three-dimensional discrete element modeling. Simulating the whole chamber with a realistic particle size requires a large number of particles, which leads to a large computational time. Both 90° and 30° segments of a calibration chamber were used in this study to reduce computational time. The effect of particle shape was simulated by prohibiting particle rotation or using simple two-ball clumps. Prohibiting particle rotation was found to increase tip resistance significantly compared with free particle rotation, and replacing a single sphere with different shapes of simple two-ball clumps was also found to have an important effect on the tip resistance. Particle crushing was simulated during CPTs by replacing a broken particle with two new equal-sized smaller particles. The results showed that there was a considerable reduction i...

Discrete element modelling of scaled railway ballast under triaxial conditions

The aim of this study is to demonstrate the use of tetrahedral clumps to model scaled railway ballast using the discrete element method (DEM). In experimental triaxial tests, the peak friction angles for scaled ballast are less sensitive to the confining pressure when compared to full-sized ballast. This is presumed to be due to the size effect on particle strength, whereby smaller particles are statistically stronger and exhibit less abrasion. To investigate this in DEM, the ballast is modelled using clumps with breakable asperities to produce the correct volumetric deformation. The effects of the quantity and properties of these asperities are investigated, and it is shown that the strength affects the macroscopic shear strength at both high and low confining pressures, while the effects of the number of asperities diminishes with increasing confining pressure due to asperity breakage. It is also shown that changing the number of asperities only affects the peak friction angle but not the ultimate friction angle by comparing the angles of repose of samples with different numbers of asperities.