## 3 Some Relevant Simulation Technologies in DDA  
Discontinuous deformation analysis (DDA) [22] is a numerical method for analyzing the discontinuous deformation of a block system. DDA constructs equilibrium equations for dynamic problems in an incremental form based on the principle of potential energy minimization. It introduces the real inertia force and uses a dynamic method to solve static (including quasi-static) and dynamic problems. For static problems, damping is adopted to absorb the kinetic energy of the block system in order to achieve a final static equilibrium state. Since it can simulate the actual mechanical process (the current static state of the block system is actually the result of a series of dynamic processes) of rock masses, the calculated results, including the contact forces between the blocks and the displacements, are of practical significance. Owing to the great advantages brought by the simulations of large deformation and discontinuous deformation in the DDA method, the blocks are allowed to move and deform as time progresses, and the mode of failure (if any) of the rock mass simulation model becomes apparent without the need to involve preliminary assumptions.  
DDA meets three convergence conditions: convergence of the equilibrium equations, convergence of the open-close iterations for all contacts, and convergence of the maximum displacement for static computations [23]. In each computation step, it usually needs several open-close iterations to adjust the contact patterns of opening, closing, or sliding until the contact pattern at each contact position does not change. By applying or removing the rigid springs on the interfaces between blocks, the contact patterns satisfying non-entrance and non-tension between blocks are realized. Then, the computation proceeds to the next step. Thus, in each open-close iteration analysis of each time step, DDA must solve the global equilibrium equations. The open-close iteration ensures that the conditions of non-entrance and non-tension are strictly obeyed among the blocks. Hence, the theory is rigid and of high computation efficiency.  
Ever since DDA was first proposed, it has received extensive attention and attracted considerable interest. Many studies on physical model testing and DDA verification [7; 8; 24; 25; 26; 27], block contact problems [9; 10; 28], three-dimensional DDA methods [11; 29; 30; 31], dynamic stability analysis [32; 33; 34; 35; 36], and engineering applications [12; 13; 37; 38; 39; 40] have been carried out.  
Even though DDA is a powerful analysis tool for the stability evaluation of rock engineering, it has not been as widely employed in practice compared to other popular numerical computation methods due to the relative difficulties with respect to its theoretic bases and the fact that it usually requires application technologies.  
For this study, a method for viscous boundary setting for calculating the dynamic deformation of a slope under seismic loading and an algorithm for modeling a pre-stressed cable were embedded into the DDA computer code. The effect of the reinforcement for the slope under seismic loading was also simulated and discussed.