A general continuum modelling approach for variable shear stress as a separable function in stored bulk solids

Granular materials stored in a bin exert pressure on its walls. The Janssen equation describes how this pressure changes with depth in a deep column of granular material. However, it does not address any change in lateral stress throughout stored bulk materials. In this work, we present a general approach for vertical and arbitrary lateral stress in the horizontal (radial) direction. The vertical and lateral stress are described by independent one-dimensional functions whose product describes the stress state throughout the entire bin. Our approach is general, and able to accommodate numerically defined functions such as splines. We are planning future experiments to determine the form of the radial stress. We report on the mathematical analysis here. This research will potentially impact the designing of bulk storage structures, inform grain drying processes and aid in inventory management of stored grain.