The idea behind Janssen's theory is that in a grannular system the walls are able to support some of the weigt of the column through frction between the walls and the particles. This leads to a non-linear relationship between the mass added to the silo, \(M_{total}\), and the measured mass at the bottom of the silo, \(M_{apparent}\). \( M_{apparent} \simeq \frac{\pi}{2} D^3 \rho (1-e^{-M_{total}/(\rho \pi D^3/8)}) \) where \(\rho\) is density of the ganular media and \(D\) is the diameter of the silo.