Granular Arch Shapes in Storage Silo Determined by Quasi-static Analysis under Uniform Vertical Pressure

Abstract

Janssen's bin effect has a great impact to a wide range of engineering applications and theoretical developments which relate to granular materials. The problem of storage silo under uniform vertical pressure exerting on horizontal cross section was investigated in two-dimensional system of equilibrium. Two choices of vertical plane where a ratio of radial stress to normal stress is constant are considered based on Janssen's approach as well as Jaky's approach. Exact stress solutions based on both approaches are generalized in cylindrical coordinates and are validated with boundary conditions at the top layer and at the great depth of silo. Despite of similar solutions obtained at the great depth, it was found that a constant coefficient of lateral pressure must be applied to the center line as suggested by Jaky, implying storage silo is stable in at-rest state. Then, the arch shapes formation in granular materials stored in silo was analyzed by quasi-statics under Jaky's approach. It was found that stacks of arch appear in variable shapes for different depths but tend to curve like catenary shape at the great depth.