Abstract: The original discontinuous deformation analysis (DDA) takes the first-order approximation of the incremental displacement to update block configuration, deduces related sub-matrices, and directly superimposes the incremental strains calculated at different time steps, which generates significant errors when simulating large rotation of a block. In order to consider the coupling effect of block rotation and deformation, a modified incremental displacement formulation is introduced, which calculates the displacements caused by the strains before the rigid-body rotation term. The sub-matrix of the inertial force is then modified, and the centrifugal and Coriolis forces are added to the load matrix. In the calculation, the coordinate transformation is carried out for the strain components and its related variables, and the newly introduced displacement formulation is used to calculate the displacements of block vertices. After that, the post-adjustment and post-contact adjustment are used to update the block configuration. The numerical examples indicate that the modified DDA can eliminate the errors caused by large rotation, automatically consider the deformation caused by centrifugal and Coriolis forces of the rotating block, and the precision of strain calculation is higher than that of original DDA. The modified codes overcome the free volume expansion and strain distortion problems, and give a reasonable block strain.

Key words: discontinuous deformation analysis (DDA), rotation error, coordinate transformation, centrifugal force, Coriolis force