Stress distribution in the material and development of loads on the wall during hopper filling

Stress distributions developing in granular materials in hoppers during the process of filling is fundamental for an understanding of the phenomena observed in hoppers. Predictions of such stress distributions are therefore essential. In this paper, based on a model which was created to simulate various filling procedures, an (ABAQUS) analysis has been carried out to investigate the development of stress distribution in the material and the loads on the hopper wall when the hopper is filled by the concentric-filling method. Calculations have been carried out either according to a procedure known as "switch-on" or according to the so-called layer-by-layer procedure. It was found that the maximum stress developed at the end of the filling, not at the bottom, but somewhere in the lower area of the hopper (layer 3). The stresses developed during layer-by-layer filling were greater than those developed during the switch-on filling in the lower area of the hopper, but were smaller in its upper area. Maxima of normal pressure along the wall were not at the outlet, even from the very beginning of filling. Instead, it was located at a position around 2/5 of the length of the wall from the outlet when the filling was finished. Various filling methods would have an effect on the stress distribution within the material and, consequently, affect the type and magnitude of loads on the hopper wall, and particularly at the hopper outlet.