Stochastic stresses in granular matter simulated by dripping identical ellipses into plane silo

A two-dimensional silo pressure model-problem is investigated by molecular dynamics simulations. A plane silo container is filled by a granular matter consisting of congruent elliptic particles dropped one by one into the silo. A suitable energy absorbing contact force mechanism is activated during particle collisions and collisions against the walls. After a while the residual kinetic energy is small enough that the granular medium can be considered to be in equilibrium. The sample of contact forces along the wall and the average vertical force components over the horizontal cross-sections through the granular matter in the silo are compared to the solution of a stochastic equilibrium differential equation. In this equation the stochasticity source is a homogeneous white noise gamma-distributed side pressure factor field along the walls. This is a generalization of the deterministic side pressure factor proposed by Janssen in 1895. The stochastic Janssen factor model is shown to be fairly consistent with the observations from which the mean and the intensity of the white noise is estimated by the method of maximum likelihood using the properties of the gamma-distribution. Two wall friction coefficients are determined, one for transforming the expectation and the other for transforming the intensity of the transverse stress factor into the mean and the intensity of the vertical white noise shear stress factor field along the walls. The latter is determined by the observed ratio of the standard deviations of the two fields. The first is estimated by fitting the exponential expectation function for the average normal stress in the horizontal cross-sections to the observed sample function by the principle of least square. Knowing these, in total four, estimated parameter values, the stochastic model determines the expectation function of the stress field normal to the walls, and the covariance functions of all considered stress fields. The observed stress field realizations are not contradicting these predictions. Thus it is demonstrated that molecular dynamics simulations can lead to valuable insight with respect to granular matter behavior even with the limited number of particles that can be handled with practicable computer efforts. Most important is the observation that a gamma-distributed stochastic side pressure field is a valid modeling assumption.