Empirical assessment of the critical time increment in explicit particulate discrete element method simulations

This contribution considers the critical time increment (〖∆t〗_crit) to achieve stable simulations using particulate discrete element method (DEM) codes that adopt a Verlet-type time integration scheme. The 〖∆t〗_crit is determined by considering the maximum vibration frequency of the system. Based on a series of parametric studies, 〖∆t〗_crit is shown to depend on the particle mass (m), the maximum contact stiffness (Kmax), and the maximum particle coordination number (CN,max). Empirical expressions relating 〖∆t〗_crit to m, Kmax, and CN,max are presented; while strictly only valid within the range of simulation scenarios considered here, these can inform DEM analysts selecting appropriate 〖∆t〗_crit values

Contact based void partitioning to assess filtration properties in DEM simulations

Discrete element method (DEM) simulations model the behaviour of a granular material by explicitly considering the individual particles. In principle, DEM analyses then provide a means to relate particle scale mechanisms with the overall, macro-scale response. However, interpretative algorithms must be applied to gain useful scientific insight using the very large amount of data available from DEM simulations. The particle and contact coordinates as well as the contact orientations can be directly obtained from a DEM simulation and the application of measures such as the coordination number and the fabric tensor to describe these data is now well-established. However, a granular material has two phases and a full description of the material also requires consideration of the voids. Quantitative analysis of the void space can give further insight into directional fabric and is also useful in assessing the filtration characteristics of a granular material. The void topology is not directly given by the DEM simulation data; rather it must be inferred from the geometry of particle phase. The current study considers the use of the contact coordinates to partition the void space for 3D DEM simulation datasets and to define individual voids as well as the boundaries or constrictions between the voids. The measured constriction sizes are comparable to those calculated using Delaunay-triangulation based methods, and the contact-based method has the advantage of being less subjective. In an example application, the method was applied to DEM models of reservoir sandstones to establish the relationship between particle and constriction sizes as well as the relationship between the void topology and the coordination number and the evolution of these properties during shearing

Empirical assessment of the critical time increment in explicit particulate discrete element method simulations

This contribution considers the critical time increment (〖∆t〗_crit) to achieve stable simulations using particulate discrete element method (DEM) codes that adopt a Verlet-type time integration scheme. The 〖∆t〗_crit is determined by considering the maximum vibration frequency of the system. Based on a series of parametric studies, 〖∆t〗_crit is shown to depend on the particle mass (m), the maximum contact stiffness (Kmax), and the maximum particle coordination number (CN,max). Empirical expressions relating 〖∆t〗_crit to m, Kmax, and CN,max are presented; while strictly only valid within the range of simulation scenarios considered here, these can inform DEM analysts selecting appropriate 〖∆t〗_crit values

Influence of the coefficient of uniformity on the size and frequency of constrictions in sand filters

Constrictions between voids control the filtration and permeability properties of granular materials. This study uses high-resolution microcomputed tomography images and discrete-element modelling to analyse two important characteristics of constrictions in granular filters: (a) the constriction size distribution (CSD) and (b) the constriction density per unit volume. The results demonstrate the importance of the particle size distribution (PSD) and void ratio of the granular material in determining the constriction density, with more widely graded materials having more densely spaced constrictions. The PSD is shown to be the main determinant of the CSD, in agreement with previous studies. The data are used to examine proposed approaches to estimate constriction spacing or void size

Constriction size distributions of granular filters: a numerical study

The retention capability of granular filters is controlled by the narrow constrictions connecting the voids within the filter. The theoretical justification for empirical filter rules used in practice includes consideration of an idealised soil fabric in which constrictions form between co-planar combinations of spherical filter particles. This idealised fabric has not been confirmed by experimental or numerical observations of real constrictions. This paper reports the results of direct, particle-scale measurement of the constriction size distribution (CSD) within virtual samples of granular filters created using the discrete-element method (DEM). A previously proposed analytical method that predicts the full CSD using inscribed circles to estimate constriction sizes is found to poorly predict the CSD for widely graded filters due to an over-idealisation of the soil fabric. The DEM data generated are used to explore quantitatively the influence of the coefficient of uniformity, particle size distribution and relative density of the filter on the CSD. For a given relative density CSDs form a narrow band of similarly shaped curves when normalised by characteristic filter diameters. This lends support to the practical use of characteristic diameters to assess filter retention capability

Using DEM to assess the influence of stress and fabric inhomogeneity and anisotropy on susceptibility to suffusion

Underfilled and gap-graded soils are known to be susceptible to suffusion; a form of internal instability in which the finer fraction of a soil is washed out from the coarser matrix under the action of seepage. This phenomenon poses a risk to embankment dams and flood embankments. The processes and mechanisms operate at the particle scale, and insight can be gained via the particulate discrete element method (DEM). Vir-tual samples can be created using DEM and simulation results can provide information on particle stresses, as well as quantitative information on the fabric of the particulate material. This is important as the amount of stress carried by the finer particles is thought to govern the susceptibility of a given material to suffusion. DEM modelling can also provide information on variation in properties within samples as well as the detailed data needed to quantify the material fabric. DEM models are, however, an idealization of reality and con-strained in particular by the number of particles used and sample preparation method. This study examines key issues relating to the development of virtual samples for use in DEM analysis and also examines the proportion of the applied stress that is carried by the finer particles

Measurement of constriction size distributions using three grain-scale methods

The grain-scale justification for empirical rules for granular filters has largely been based on simplified models of sphere packings. The development of discrete element modelling (DEM) and micro computed tomography (μCT) enables a more scientific appraisal of the void space within granular filter materials. The constrictions or pore throats that govern the filter’s performance can now be directly measured. However, definitive partitioning of the void space is not possible for realistic grain packings and so multiple methods, with differing theoretical bases, have been proposed to identify constrictions. This contribution compares three such methods, each of which results in a constriction size distribution (CSD). The methods considered are the triangulation based weighted Delaunay method (Reboul et al. 2010), a contact based method (O’Sullivan et al. 2015) and an image analysis method based on watershed segmentation (Taylor et al. 2015). Each model, along with its relative advantages is introduced. Then CSDs resulting from applying each model to the same virtual filter samples created using DEM are presented. It is shown that there is reasonable agreement despite the different basis of each approach. A consideration of empirical filter rules is carried out by normalising the full CSDs by the characteristic diameters typically used to represent the retention capacity of granular filters in design. It is shown that similar CSD curves are obtained for different particle size distributions (PSDs) when curves are normalised by characteristic diameters, irrespective of the method used to identify the constrictions. This gives fundamental support to filter rules using characteristic particle diameters to represent the filtration capability of granular filters

A Variational Integrator for the Discrete Element Method

A novel implicit integration scheme for the Discrete Element Method (DEM) based on the variational integrator approach is presented. The numerical solver provides a fully dynamical description that, notably, reduces to an energy minimisation scheme in the quasi-static limit. A detailed derivation of the numerical method is presented for the Hookean contact model and tested against an established open source DEM package that uses the velocity-Verlet integration scheme. These tests compare results for a single collision, long-term stability and statistical quantities of ensembles of particles. Numerically, the proposed integration method demonstrates equivalent accuracy to the velocity-Verlet method