Discrete element simulations of floor pressure due to a granular material in a cylindrical vessel

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.