Numerical modelling of quaking in tall silos

Quaking in tall mass flow silos is a significant problem faced by industry, and can be treated as a simple one-dimensional system. In this paper, quaking in tall silos is examined using a dynamic version of Janssenʹs equation, based on a one-dimensional version of a hypoplastic constitutive model. This model is used to examine the motion of rarefaction waves such as those present at the beginning of each quake cycle, and the numerical solutions for this system show many features in common to experimental findings from previous studies. In particular, the model shows the same exponential growth of the amplitude of quakes with the height of the silo, as that observed experimentally. Through this model the role of wall friction in the quaking process can be understood.