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294 Ch a p t e r N i n e

9.3 Shape Representation and Computational Efficiency Enhancement
Due to the complexity to model the real particles in 3D, spheres, ellipsoids, or discs are
usually used in DEM simulations instead of complex particles. However, particle shape
is an important factor that affects the interlock among the particles and other properties
of the materials. It is necessary to build more sophisticated models that consider the
particle shape effects. In recent years, some research has been carried out to study the
effect of particle shape. Attempts were made to simulate elliptical systems both in 2D
(Rothernburg, 1992) and 3D (Lin and Ng, 1997). More complicated particle shapes may
be modeled using superquadrics (Williams and Pentland, 1991) or bonding a number of
spheres together (Walton and Braun, 1993). Jensen et al. (2001a, b) presented a detailed
computational investigation of the effect of particle shape on the interface shear behav-
ior of granular materials. Clusters made of several discs were applied to model the
rough particles using DEM simulation. Seven cluster shapes of varying degrees of
roughness were presented in his paper. However, simulating real materials made up of
a very large number of particles with complex shapes is currently still a challenge in
DEM modeling. The method presented in this section provides a practical way to rep-
resent the particles with complex shapes, which makes it possible to build more sophis-
ticated models that can consider the particle shape effects.

9.3.1 Basic Idea of Clustering
A particle with a complex shape can be modeled by combining smaller discs in 2D or
spheres in 3D into a cluster with a similar shape, shown in Figure 9.8.
3D
In PFC , spheres within a cluster are allowed to overlap to any extent, but each
cluster still behaves as a rigid body with deformable boundaries. Contacts internal to
the cluster are skipped and not affected during the calculation cycle. Contact forces are
not generated between those spheres within the cluster and the contact forces that exist
when a cluster is created or when a sphere is added to the cluster remain unchanged
during computational processes. For more details of the PFC program, please see the
3D
Itasca Manual 5.0 (Itasca, 2005).
9.3.2 Idea of Representing Particles Using X-ray Tomography Imaging
As illustrated in Chapter 3, X-ray tomography imaging is a powerful tool to character-
ize the inside structure of materials. It has been widely applied to study the microstruc-
ture of geomaterials in recent years. The specimen is scanned using X-ray layer by layer
(or cone beam) and the location of each particle in each layer is recorded pixel by pixel.

) a ( ) b (
(a) Outline of a Real Particle with Complex Shape (b) Cluster Made up of Smaller Balls

FIGURE 9.8 Illustration of clustering.