Correlation of microscopic and macroscopic elastic constants of granular materials based on linear contact model

For the discrete element method (DEM), the key to a successful simulation lies in proper micro-parameters. However, the current way to select micro-parameters is often subjective and unreliable, resulting in incomparability among different simulations. Based on the linear contact model, a set of empirical formulas are presented to describe the correlation between macroscopic elastic constants of granular materials and microscopic elastic constants of particles by simulating tri-axial tests with PFC3D and through regression analysis of numerical results. The macroscopic elastic constants include the initial Young’s modulus and the initial Poisson’s ratio, and the microscopic elastic constants include the normal stiffness, stiffness ratio of particle, etc. It is found that the initial Young’s modulus and the shear modulus are approximately proportional to one tenth power of the confining pressure, and inversely proportional to nine tenths power of the particle size. The initial Poisson’s ratio is approximately proportional to one fourteenth power of the stiffness ratio of the particle for the linear contact model, and almost independent of the particle size. It is also found that the rational stiffness ratio of the particle ranges from 2.0 to 20.7 for the common sand.