Study on the Damping of the Discontinuous Deformation Analysis Based on Two-Block Model

The deformation and failure of rock mass is a process of energy dissipation; the damping of DDA is a very important and basic problem. The correctness and effectiveness of DDA rely on the appropriate values of the numeric controlling parameters like time interval, spring stiffness, and assumed maximum displacement ratio , and the contact using the penalty method is the core content of DDA. A mechanical model of two contact blocks loaded with the normal force acting along one side of block boundary is established to study the DDA damping problem, which involves the contact and eliminates the influence of some numeric control parameters (e.g., ). Based on the Newmark method and the theory of DDA, the motion equations of two-block system can be established, and then the relationship of some numeric control parameters and the influence of damping can be obtained. The algorithmic damping increases with the increasing of time interval. Given a very small time interval, the spring stiffness may have no obvious effect on the algorithmic damping. The numerical results reveal that the essence of time interval influencing the open-close iteration is the fact that the algorithmic damping is mainly controlled by time interval.