When dynamic time-history calculations are carried out by using the particle discrete element method (DEM)

the absorption boundary condition must be applied to avoid the reflection of outward propagating waves back into the model at artificial boundaries. By considering the various radius of particle elements on the artificial boundaries and their uneven boundary surfaces

the equivalent equations for DEM is obtained based on the boundary conditions of the viscous and viscoelastic continuum and free field. Calibration factors are introduced into the equivalent equation of viscous boundary condition for DEM

and a ratio-iterative method is proposed to determine the values for optimum waves absorption quickly. Numerical models for the viscous

viscoelastic and free-field boundaries are established using the 2D particle flow code (PFC2D). We also analyze the effects of particle distribution patterns on the radius and velocity of particles on the viscous boundary and the process of the ratio-iterative method. The validity of the setting method for viscoelastic boundary condition is verified with examples of the external source problem and the Lamb problem. The free-field boundary for DEM is applied to a tunnel example for the validation.