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.