Calibration of discrete element modeling: Scaling laws and dimensionless analysis

In this paper, dynamic similarity conditions are derived for discrete element simulations by non-dimensionalising the governing equations. These conditions must be satisfied so that the numerical model is a good representation of the physical phenomenon. For a pure mechanical system, if three independent ratios of the corresponding quantities between the two models are set, then the ratios of other quantities must be chosen according to the similarity principles. The scalability of linear and non-linear contact laws is also investigated. Numerical tests of 3D uni-axial compression are carried out to verify the theoretical results. Another example is presented to show how to calibrate the model according to laboratory data and similarity conditions. However, it is impossible to reduce computer time by scaling up or down certain parameters and continue to uphold the similarity conditions. The results in this paper provide guidelines to assist discrete element modelers in setting up the model parameters in a physically meaningful way.