“…According to existing literatures [10,[26][27][28], equations for contact force, damping force, friction force, and torque used here are listed in Table 1, where, R* is the equivalent radius; E* is equivalent Young's modulus; E is Young's modulus; υ is Possion's ratio; δ n is normal particle overlap; is a unit vector from the center of the particle to the contact point; m ij is equivalent mass; v n,ij is the normal relative velocity of particle i and j; μ s is sliding frictional coefficient; δ t,ij is the particle tangential overlap; δ t,ij ,max is the maximum particle tangential overlap; is the unit vector of particle tangential overlap; v t,ij is the tangential relative velocity of particle i and j; R ij is the vector from the mass center of particle i to particle j; μ r,ij is rolling friction coefficient;…”