Abstract: This paper aims at establishing a set of scaling laws according to three similarity criteria of geometric similarity, mechanical similarity, dynamic similarity, under which a scaled discrete element model can exactly reproduce the prototypical problem. The method is based on the exact scaling laws of discrete element method proposed by Prof. Y. T. Feng. The scaling laws are then extended to the study of rheological behavior of granular materials. A detailed theoretical derivation is given based on the Burgers creep model. The rheological parameters are introduced to the model, and then we can gain the scaling laws in both two-dimensional and three-dimensional cases. Secondly, numerical simulation is conducted on the basis of the theoretical derivation. The results show that some parameters must be scaled to ensure the consistence of simulated results. The scaled discrete element model can exactly represent the original physical problem within the relative error of 3%. This paper also discusses the influence of the time step, viscosity coefficient, particle numbers and scale number on numerical simulation, which provides a good reference for parameters selecting in numerical simulations. Besides, because the scaled model has the same particle number, particle shape, particle compactness and scale number as the physical model, it can reveal the effect of proportional scaling on rheological behaviors.

Key words: discrete element method (DEM), granular material, exact scaling, equal proportional scaling, rheological analysis