Model for the prediction of grain density and pressure distribution in hopper-bottom silos

A model was developed to predict the grain density, pressure distribution and grain mass in hopper-bottom silos. The model consisted of a series of differential equations derived from the force equilibrium on a differential element of grain in the silo. These differential equations govern the relationship between the variable grain density and the stresses in the grain mass. An oedometer was used to measure the bulk density of wheat under various pressure levels. Based on the experimental data, a quadratic equation was proposed to model the relationship between the grain density and the maximum principal stress. The model predicted that grain density, and vertical and lateral pressures in the grain mass increased with the grain depth in the cylindrical portion of the hopper-bottom silo, but decreased with the depth in the hopper. The lateral pressure predicted by the model was greater than that calculated by the Janssen equation for the cylindrical section of the silo. The model predictions of grain mass in silos were compared with the measured values from commercial grain silos at two locations, and differences were found to be less than 1.45%.