ANALYSIS OF PRESSURE EVOLUTION IN GRANULAR MATERIALS IN CONVERGING BINS DURING FILLING AND EMPTYING PROCESSES

Abstract

A simplified analysis of deformation and stress states in converging hoppers during filling and discharge of granular material is presented. In particular we discuss a method for solving the set of differential equations governing the flow of granular material in a plane wedge hopper. The equilibrium conditions and stress-strain relations are satisfied for the planar slice elements assuming the dependence of displacement and stress on the Cartesian coordinate z. The transient flow of an icompressible, non-cohesive granular material in a two-dimensional converging hopper is considered. We assume the material to be in elastic or elasto-plastic states within the hopper satisfying the Coulomb yield condition and the non-associated flow rule. The paper presents a detailed analysis of the evolution of pressure acting on the hopper wall during the filling and emptying processes when the initial active state of pressure is transformed into a passive state. Analytical and numerical analyses are presented. It is shown that at the initial stage of the emptying process a considerable switch overpressure develops, exceeding the steady-state passive pressure several times.