Displacement Accuracy of Discontinuous Deformation Analysis Method Applied to Sliding Block

Discontinuous deformation analysis (DDA) is a discrete element method that was developed for computing large deformation in fractured rock masses. In this paper, we present an alternative derivation of the basic theory of DDA for planar (two-dimensional) problems, and we address the accuracy of the DDA method for sliding blocks using sensitivity analyses. Results of analyses with different parameters show that the residual and relative errors in the displacement of a frictional sliding block are controlled by the perturbation in the initial time steps of the simulation. In addition, we expose a systematic error induced by the DDA penalty formulation. Overall, the initial perturbation of the solution decreases with decreasing friction angle and increasing contact penalty and, counterintuitively, decreases with increasing time step size. All analyses show that the long runout behavior of the system trends toward the analytic solution, independent of the initial perturbation. The resulting precision of the long runout simulation is more than sufficient for all problems of engineering interest.