Extensions of discontinuous deformation analysis for jointed rock masses

Beginning with the original work of Shi [Discontinuous deformation analysis: a new numerical method for the statics and dynamics of block systems. Ph.D. thesis, University of California, Berkeley (1988)], called the Discontinuous Deformation Analysis (DDA) method, a number of extensions to the method have been explored. The extensions consist of improving the contact algorithm, adding block fracturing and sub-blocking capabilities. Contacts between blocks have been modeled using an Augmented Lagrangian Method instead of the penalty method originally proposed by Shi. This allows block-to-block contacts to be enforced more precisely and block contact forces to be determined more accurately. A sub-blocking capability has been developed, whereby blocks are discretized into sub-blocks. The continuity of the sub-block contacts is preserved and the variation of stresses in each large block can be determined. The sub-blocking capability is done using a consistent formulation in which the same methodology is used for the sub-blocks as the original large blocks. This is different from other discrete block methods that imbed finite difference zones or finite elements inside larger blocks. Finally, two block fracturing algorithms have been implemented in the DDA method. Using a three-parameter (cohesion, friction, tensile strength) Mohr-Coulomb criterion, one algorithm allows intact rocks to be broken into smaller blocks. Fracturing can be in shear or tension. The second algorithm allows fractures to propagate in the sub-blocks either in Mode I (tensile fracturing) or Mode II (shear fracturing). All three extensions have been implemented into the original DDA program of Shi. With the three extensions, the DDA method is more applicable to a greater range of rock mechanics problems and other engineering problems involving blocky systems. Examples of application of the method, for plane stress condition, are presented with regard to rock fall, slope stability and underground excavation problems.