An efficient technique for generating homogeneous specimens for DEM studies

doi:10.1016/S0266-352X(03)00064-8

Computers and Geotechnics

Volume 30, Issue 7, October 2003, Pages 579-597

https://doi.org/10.1016/S0266-352X(03)00064-8 Get rights and content

Abstract

A new technique, designated as the Multi-layer with Undercompaction Method (UCM), capable of generating homogeneous specimens for DEM studies is presented herein. The specimen are compacted in several layers using undercompaction criteria based on average planar void ratio. The proposed approach was compared to other available methods and was proven to generate very homogeneous specimens provided a nonlinear average undercompaction criterion was used. Furthermore, the UCM method was efficient for a variety of density conditions ranging from very loose to dense states.

Introduction

Natural soils consist of particles, macropores, micropores, pore fluids (air, water, others), assembled with interparticle bonding to form a fabric. The behaviour of natural soils is complex and difficult to describe adequately by conventional non-linear elastic models or elasto-plastic models. In order to gain some insight into the behaviour of these soils, micro-mechanics may prove helpful.

In the past, two approaches were used to study particle interaction using micromechanics. The first one uses laboratory experiments on natural sand or rods to observe the changes in the contact distribution within the specimen [1], [2], or in shear bands [3]. Problems with laboratory experiments are apparent: inability to prepare exact replicates of the physical system, difficulty to observe the microstructural response of the grain arrangement under undrained loading, i.e. with pore water generation [4]. The second approach simulates the soil using the Distinct Element Method (DEM) as proposed by Cundall et al. [5], [6]. DEM is able to monitor the evolution of internal stresses and contact behaviour in a non-destructive manner. It also facilitates sample reproducibility. Since external stresses and stress paths can be controlled, it is ideal for understanding the fundamental behaviour of given particle assemblages during any type of loading and it may be used to develop and validate constitutive relationships for soils.

Since the pioneering work carried out more than two decades ago [5], [6], DEM has proven to be a useful tool that was applied in many fields, such as fluid dynamics and particularly soil mechanics. A general overview was presented in reference [7] on the application of DEM to granular media. Research work in DEM related to soil mechanics can be mainly grouped into the following areas:

1.
Static behaviour of granular media using different particle shapes: disks [8]; 2-D elliptical or oval shaped particles [9]; angular elements [10]; disk-clusters [11]; disks with rolling resistance [12]; 3-D spheres [13], [14]; 3-D ellipsoids [15]. These studies were performed with elastic contact laws based on Hertzian theory for 3-D codes, while linear-elastic contact laws were used in 2-D codes.
2.
Clay behaviour in compression using slate-shaped particles and considering repulsive force between particles [16], including mechanism of macro-anisotropy and micro-anisotropy in cohesive soils [17]; or viscous creep behaviour of soil by considering interparticle sliding with both viscous and frictional component for the contact laws [18].
3.
Strain localisation of granular materials during shear using disk shaped particles [19], [20], [21], [22] and disks with a rolling resistance [23].
4.
Dynamic behaviour and liquefaction of regularly-packed disk assemblies [24], [25] and randomly-packed disk assemblies using the “quasi-pore pressure” method [26], [27].

Except for the works on granular soils by a few researchers [28], all other DEM analyses were carried out on densely-packed granular specimens. Peculiar behaviours of natural soil, as well as liquefaction and static collapse in loose sand, are areas of great interest for the geotechnical engineers. Because current techniques used for generating specimens hardly result in homogeneous loose/medium specimens, as will be shown below, the first task before studying peculiar behaviours of natural soil and liquefaction phenomena in granular media was to develop an efficient technique to generate homogeneous loose/medium specimens for DEM studies.

In this paper, different techniques for DEM sample generation are studied, especially with respect to sample homogeneity. A new DEM technique, referred to as the multi-layer with undercompaction method (UCM), is proposed to generate homogeneous specimens for DEM studies. The paper also discusses the adequacy of various undercompaction criteria including that proposed in the literature [29] and introduces a new criterion especially useful for DEM sample generation.

Section snippets

Current techniques

Load is sustained in an assembly of particles through contact between particles. Particle data (shape, position, size, density, number, grain size distribution,velocity of particles…) and contact data (particles in contact, force, position, number of contact…) are the two types of input data to consider for the analysis of any particle assembly under different loading conditions but also for generating a specimen. Four different techniques are available for specimen generation: (1) Fixed Point

UL DEM code

The DEM code developed at Université Laval (U.L) is a two-dimensional code similar to that proposed in Refs. [5], [6]. Each rigid disk is identified separately, with its own mass, moment of inertia and contact properties. Normal and tangential springs and dashpots exist at each contact, including interparticle contact and particle/wall contact illustrated in Fig. 1.

In Fig. 1, a divider is included in order to allow for no contact forces between two particles if they separate. A slider

Generation of initial particle arrangement

The numerical method of simulating randomly-packed material is shown in Fig. 6 as a flow chart for particles corresponding to a specific grain size distribution. To form ‘pseudo-random decimal’ in a numerical simulation, which should be homogeneously distributed in (0, 1), a random number, z_i, was generated using the following relation: $z_{i} = a·z_{i−1} mod M$ where, a is non-negative multiplicator, M is parameter. (mod M) means the residual number after (a·z_i) being divided by M. i represents order number

Undercompaction criteria

One important issue for the multi-layer with undercompaction method is the undercompaction criterion used to determine the required compaction degree for each layer. The average undercompaction value was determined based on trial and error, which is time consuming. To make the multi-layer with undercompaction method readily useable in other DEM analyses, a pre-established compaction criterion may prove useful.

Ladd [29] defined a predetermined percent undercompaction for each layer, U_n, which is

Conclusions

In this study, a new technique, designated as the Multi-layer with Undercompaction Method (UCM) was described. Its objective was to generate homogeneous DEM specimens for a variety of density conditions ranging from very loose to dense states. Particles are divided evenly to form several layers and compacted layer by layer. When compacting the nth layer, all n layers are compacted to a state looser than the final target value in order to reduce the effect of compaction energy transferred from

Acknowledgements

The authors thank the National Science and Engineering Research Council, Canada, for the financial support of the first author.

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View full text

An efficient technique for generating homogeneous specimens for DEM studies

Abstract

Introduction

Section snippets

Current techniques

UL DEM code

Generation of initial particle arrangement

Undercompaction criteria

Conclusions

Acknowledgements

Soils and Foundations

Computers and Geotechnics

International Journal of Non-Linear Mechanics

Powder Technology

Photoelastic verification of a mechanical model for the flow of a granular material

J. Mech. Phys. Solids

Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography

Geotechnique

Microscopic analysis on artificially-prepared structured collapsible loess

Chinese Journal of Geotechnical Engineering

The distinct numerical model for granular assemblies

Geotechnique

Discrete numerical model for soil mechanics

Journal of Geotechnical Engineering, ASCE

Micromechanical features of granular assemblies with planar elliptical particles

Geotechnique

Capturing nonspherical shape of granular media with disk clusters

Journal of Geotechnical and Geoenvironmental Engineering, ASCE

Importance of particle rotation in the mechanics of granular materials

Axisymmetric compression of 3-D polydisperse systems of spheres