Analysis of pressure evolution in granular materials in converging bins during filling and emptying processes

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, cohesionless 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.