ABSTRACT: At the end of the 19th century, H. A. Janssen discovered that the floor pressure in a cylindrical container of granular material asymptotes exponentially to a value less than the weight of the material i.e., the pressure becomes independent of the fill height of the column. This phenomenon is investigated using discrete element simulations of inelastic, frictional spheres in a cylindrical vessel having a particle-to-cylinder diameter ratio at approximately 13.3 or 26.6, with varying bed heights in both cases. The load experienced by a piston that is supporting the granular column are computed. In order to activate frictional forces at the wall contacts either the piston (or equivalently the cylinder wall), is slowly displaced at a constant rate so as to maintain quasi-static conditions. Various combinations of wall and interparticle friction coefficients are examined. The simulated behavior of the load vs. fill level was found to fit well to the functional form of Janssen's theory. Moreover, quantitative comparisons are in agreement with experimental measurements from the literature. The effect of a tangential force applied to the surface of the particles at the contact point rather than the center of the particle is also analyzed. The tangential force causes a torque on the particle, which consequently causes a rotation of the particle. The rate of rotation is proportional to the wall friction coefficient. It is shown that an increase in the wall friction coefficient may not increase the resistance to sliding. However, the increase in wall friction coefficient causes a higher particle angular velocity, which acts like lubrication at the wall causing a higher load then expected. These rotations cause a violation of Janssen's assumption that frictional forces are fully activated.

For those not familiar with the discrete element method, a quote from wikipedia:

“A discrete element method (DEM), also called a distinct element method is any of family of numerical methods for computing the motion of a large number of particles of micron-scale size and above. Though DEM is very closely related to molecular dynamics, the method is generally distinguished by its inclusion of rotational degrees-of-freedom as well as stateful contact and often complicated geometries (including polyhedra). With advances in computing power and numerical algorithms for nearest neighbor sorting, it has become possible to numerically simulate millions of particles on a single processor. Today DEM is becoming widely accepted as an effective method of addressing engineering problems in granular and discontinuous materials, especially in granular flows, powder mechanics, and rock mechanics.”

Janssen Effect

Code was developed and simulations run to try and understand the Janssen effect.  The basic geometry of the problem is shown in the image below; a granular column.   We have been able to successfully obtain quantitate comparisons between the simulations and experiments, and are in the process of some final simulations.