By using 3D discrete element simulation, a series of uniaxial compression and pure shear test were carried out on granular material with the aim to study the insufficiencies of those effective medium theories from the level of microscale of particle size and mesoscale of force chain. The simulation indicates that stress relaxation resulting from the rotation and rearrangements of particles has negligible influences on the calculation of bulk modulus. Shear stiffness calibration factor (C) and combined parameter R/R were advocated to calibrate those effective medium theories based on Hertz-Mindlin contact model to accounting for the influence of relaxation in contact area and grain angularity.