The proper modeling of granular flow using discontinuum mechanics has the potential to be one of the most significant scientific advancements in the mining industry today. The discrete element method (DEM) is the name given to solution process by which the macroscopic behavior of a system is determined by modeling its individual components.

In many instances this involves the mathematical modeling of hundreds of thousands of individual “particles” or “groups of particles”. At it most basic level Newton’s equations of motion are solved for each and every particle at incrementally small time intervals.

With the tremendous advances in computing power over the past decade, the DEM process is literally solve by “brute force”. Additionally, advanced constitutive equations have now been implemented which allow accurate modeling of both cohesive and adhesive forces (examples).

AC-Tek is a leader in this rapidly advancing technology. Our engineers and software developers have devoted an enormous amount of effect into developing the “Newton” DEM simulation software. Additionally, we have published several papers in this field, and have been involved with numerous projects using the DEM method.

The DEM method should however be applied and used no differently than any of the other "tools" an engineer has in their toolbox. It must be combined with good engineering knowledge, design experience, and a firm understanding of the characteristics of the material being conveyed.

The first step in using the DEM method is to create the bounding geometry. This can be done in a wide variety of CAD programs and then easily imported into the Newton software.

Historically, simple mathematical equations for lines and curved surfaces were often used. Other methods involve fixing or “gluing” particles to specific locations in space. The most common method however is to automatically re-mesh the surface into triangles. The flexibility of triangular surfaces allows designers to generate almost any surface shape. Triangles are also very useful in the post processing stage to determine the impact and shear forces. Furthermore, they naturally lend themselves to easy visualization and computation.

Boundary surfaces can have unique material properties such as frictional resistance and restitution coefficients. Additionally, surfaces may have fixed, or varying velocities and are even allowed to move with respect to each other (gate opening or closing for example).

When modeling any complex problem on a computer, a firm understanding of the real world parameters must be known in order to accurately represent and predict the systems behavior. In many applications the material properties themselves can vary significantly over a given time frame. This may be on a large time frame (such as summer to winter conditions), or as quickly as a few minutes (when material is belting delivered via separate sources).

Material input data screen for the
"Newton" DEM simulation software

At first this may seem to be a major obstacle when trying to predict material behavior. However, one can quickly realize that this is perhaps the greatest strength of computer modeling. For any given geometry a wide range of material properties (frictional coefficients, moisture content, cohesive properties, ect) can be modeled and compared. Varying size distributions, and even completely different material types can be simulated. Trouble areas can be spotted, and the design can be modified before ever leaving the drafting table. This is huge advantage over the historical practice of "trial and error" used in the past. Far too often the final design was the prototype and initial test bed!

Once the geometry and material properties have been entered the computers can go to work. DEM simulations can required anywhere from 5-10 minutes to solve a given problem, to days or even weeks. It simply depends on the number of particles in the simulation and the required run time. As a rule-of-thumb, a typical desktop computer is capable of solving a reasonable flow simulation in 6-12 hours.

The figure on the right is a simulation of a rapid load out terminal in South Africa. The material enters the transfer via a vibrating feeder bed. The initial particle distribution, velocity, and direction were model to match this behavior as closely as possible. This particular deign used particle sizes from 5-75mm, and over 500,0000 particles were simulated to accurately predict the flow.

"This total flexibility inherent to the DEM method is by far its most tantalizing quality. By correctly modeling the individual properties of a system, it’s complex, and often-chaotic behavior, may be analyzed, altered, and improved. The potential applications in the mining industry alone are enormous." (Ref)