: We study the accuracy of discontinuous deformation analysis (DDA) by analyzing the displacement of a single sliding block on an inclined plane over distances of 25 and 250 meters. Increasing the time step and penalty value improves the initial accuracy and decreases the relative error as the block displaces. At penalty and time step values commonly used in DDA, the solution to the DDA system of equations is found to largely depend on the accuracy of the forcing vector. At very high penalty values (e.g., 1010, 1012), the solution starts to degrade due to ill-conditioning in the DDA stiffness matrix.
1 INTRODUCTION
The discontinuous deformation analysis (DDA) proposed by Shi (1988) provides rock engineers with a tool useful for investigation the kinematics of blocky rock masses. Quantifying the accuracy of DDA as a block systems undergoes progressive dynamic deformation is important for understanding the dynamic behavior of rock masses. The sliding block on an inclined plane (Fig. 1) provides an example problem that is on one hand simple to understand, yet on the other hand exhibits a number of surprising characteristics. Using the sliding block model, several previous validation studies (Yeung 1991; MacLaughlin 1997; Maclaughlin and Sitar 1999; MacLaughlin et al. 2001) have demonstrated that DDA can be considered accurate in the sense that displacement data matches analytic solutions for simple problems (e.g., Fig. 2). However, these studies have been limited to displacements of at most a few meters. Long displacement runouts of tens to hundreds of meters, typical of landslides, have not been studied.
