It turns out that the measured wall friction, when plotted against the ratio of groove volume to particle volume (in a logarithmic scale), behaves like a three-part function. Even for crushed glass (an amorphous particle) the behavior is similar. The data distributes into three regions, two of them remaining flat and a third one having a slope. The most intriguing part is that if we divide the measured wall friction angle by the measured effective angle of internal friction, we reduce this plot to a two-part function. It starts flat and then jumps to a step that remains constant to higher values of the mentioned ratio.

But there is not an evident function that can relate these two variables clearly; there are no continuum equations from which these results can be derived. But there might be a way out, if we look at what DEM (discrete element method) does. DEM tracks every particle in the simulation, because each particle has a dynamic equation that is being solved. DEM solves thousands of dynamic equations at every pre-established time step, using the initial conditions at the boundary and then applying these values into force-displacement laws that determine the corresponding contact forces. The acceleration is determined from the forces using the dynamic equation (Newton’s Second Law), which is later integrated to find velocity and then displacement of the particles, the positions of these particles are updated, the displacement computed, and the cycle starts again.

To be continued…