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

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

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

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

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

Implementation of real contact behaviour in the DEM modelling of triaxial tests on railway ballast

In the Discrete Element modelling of soils, the micromechanical behaviour at contacts has often been considered to have a minor influence on the macromechanical response, leaving basic theoretical models (e.g., Hertz) to describe the contact response in the normal direction. A realistic description of the contact response may be crucial especially when investigating small strain ranges. Recent experimental inter-particle loading tests on gravel suggest that the classic contact models fail to reproduce certain mechanical features, especially when roughness is significant. Here, some of these experimental observations, including a softer response than the Hertz model under loading in the normal direction, and plasticity on unloading, are implemented in a DEM model for the simulation of small strain tests on railway ballast. The influence of these features on small strain stiffness is highlighted. A micromechanical analysis is carried out to show how each of the contact-level features introduced affects the macroscopic response

A study of membrane correction accounting for both curvature and tension in DEM simulations of triaxial tests of sand and ballast with two alternative flexible membrane models

In DEM simulations of triaxial tests, modelling a flexible lateral membrane is crucial and challenging. It is essential for the correct application of a uniform lateral pressure and for an accurate measurement of sample volume. Here, we introduce a membrane made of triangular facets, and model it as a continuum; we then compare this approach with a well-established method that uses a layer of bonded spheres. With either method, it is also possible to assess the additional stress applied by the membrane as it deforms, i.e. the difference between the stress applied at the boundary and the actual stress within the sample. It is shown that this difference has two origins: the tension developed in the membrane, as it deforms; and the curvature of the membrane, since this causes a vertical component of the confining pressure which can be significant. These findings may be used to inform and improve the membrane correction commonly used in experiments, where similar effects occur

Micro mechanics of isotropic normal compression

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

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