Page 293 - Mechanics of Asphalt Microstructure and Micromechanics

CHAPTER9

Applications of Discrete

Element Method

9.1 Introduction
The distinct element method, or discrete element method (DEM), was first introduced
by Cundall in the early 1970s. It was originally applied to rocks and then extended to
granular materials (Cundall and Strack, 1979). The basic idea of DEM is straightfor-
ward: application of Newton’s second law to characterize movements of multiple inter-
acting rigid bodies. The general philosophy follows the following steps: 1) assign the
initial locations and velocities to individual particles; 2) detect whether adjacent parti-
cles are in contact or not; 3) calculate the forces and moments due to contacts and other
sources; 4) compute acceleration via Newton’s second law; 5) integrate the acceleration
to update the velocity; 6) further integrate the velocity to update the positions; and
7) iterate to obtain the dynamic equilibrium conditions for all the particles. DEM has
been widely used in rock and soil, geotechnical engineering, granular materials, fluids,
and concrete. It has found more applications in asphalt concrete (AC) in recent years.
Most applications in asphalt have made use of Particle Flow Code PFC 3D or PFC 2D.
The following provides brief descriptions of some basic elements of how PFC 3D solves
a problem. There are other DEM platforms that can address irregular shapes (such as
ellipsoids and polygons) and more complicated contact models. These platforms are
not described as few researchers in AC are using them.

9.2 Fundamentals of DEM
The initial purpose of developing the DEM approach was for the verification of constitu-
tive models for granular soils. The model developed by Cundall assumes the following:
1. The particles are circular/spherical and treated as rigid bodies.
2. The contact points between particles occur over an infinitesimally small area.
3. The particles are allowed to overlap slightly at contact points.
4. The magnitude of the overlap is linearly proportional to the contact force,
unless slip or separation occurs.
5. The slip condition is provided by Mohr-Coulomb law.

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