Discrete Element Method (DEM)

The Discrete Element Method (DEM) is a numerical method used to compute the stresses and displacements in a volume containing a large number of particles such as grains of sand.

The granular material is modelled as an assembly of rigid particles and the interaction between each particle is explicitly considered (Figure 1). The particle shapes and geometries are specified by the user. Spheres or ellipsoids are commonly used.

Figure 1. DEM Particle assembly and example of mechanical model for contact point

The Finite Element Method (FEM) models the soil as a continuum and describes the soil by point wise mathematical expressions, i.e. stress in a point x: sigma(x). DEM differs therefore from FEM in that individual particles are considered.

Our software
At NGI we apply the commercial Particle Flow Code (PFC3D) for our DEM modelling. The program has been developed by Itasca Consulting Group. It allows finite displacements and rotations of discrete bodies including complete detachment and also recognizes new contacts automatically as the calculation progresses.
Some application fields of PFC3D:

fundamental studies of granular materials: yield, flow, volume changes,...
fundamental studies of solids, represented by bonded assemblies of particle: damage accumulation, fracture and acoustic emission, moment tensors,...
finite deformation analysis of granular materials

Example of application of DEM at NGI
It is known that whereas continuum-based modelling represents damages indirectly through empirical relations, the discrete element method (DEM) utilizes the breakage of individual structural units or bonds (micro-cracks) to directly represent damage. Therefore neither complex constitutive models nor a priori assumptions regarding the location and type of failure are required for reproducing the realistic material behaviour. As one example of application we have investigated the fracture mechanisms in rock materials and the acoustic emissions in that process in the project ACUPS (Figures 2 and 3).

Figure 2. An example of the calibration results of triaxial test on Vosges sandstone using the PFC3D.

Figure 3. An example of investigating fracture mechanisms in rock material using bond breakages (micro-cracks), acoustic emissions (AEs) and moment tensors