damp out real vibrations. On the other hand, the energy consumption in DDA is due to the frictional resistance at contact. By passing the velocities of the blocks at the end of a time step to the next time step, DDA gives real dynamic solution with correct energy consumption. By using an energy approach, DDA does not require an artificial damping term to dissipate energy as in DEM, and can easily incorporate other mechanisms for energy loss. Strengths and limitations DDA has several strengths recommending it for use in slope stability problems in jointed rock masses, which are balanced by serious limitations be accounted when DDA is used for larger scale, faster moving problems. Strengths Very good for problems with small characteristic as time marching scheme provides necessary numerical damping to control resonance interactions within and between particles. Step-wise linear implicit time marching allows so-called quasi-static solutions, where step-wise velocities are never used. Quasi-static analysis is useful for examining slow, or creeping failures. Limitations The most serious limitation of the DDA method is the reduction of numerical damping which occurs as the characteristic length of a problem grows. The numerically, damping is a function of . Typically, the stiffness doesn't vary over 1 or 2 orders of magnitude, while the mass is a function of the cube of the characteristic length. Modification and improvement Various modifications to the original DDA formulation have been reported in the rock mechanics literature. In the original DDA formulation a first order polynomial displacement function was assumed, so the stresses and strains within a block in the model were constant. This approximation precludes the application of this algorithm to problems with significant stress variations within the block. However, in cases where the displacement inside the block is high and cannot be ignored, the blocks can be divided by mesh. An example of this approach is the research by Chang et al. and Jing who resolved this problem by adding finite element meshes in the two-dimensional domain of the blocks so that stress variations within the blocks can be allowed. Higher order DDA method for two-dimensional problems has been developed in both theory and computer codes by researchers like Koo and Chern, Ma et al. and Hsiung. Additionally, The DDA contact model which was originally based on penalty method was improved by adopting the Lagrange type approach reported by Lin et al. Since a blocky system