Discontinuous Deformation Analysis in Rock Mechanics Practice

"This is an extended abstract for a keynote lecture delivered by the author during the 2015 ISRM congress in Montreal on the application of the numerical discontinuous deformation analysis (DDA) method in rock mechanics practice. Due to the large scope of the topic this lecture will focus on studies performed by the rock mechanics group at Ben-Gurion University, alone or in collaboration which other research groups, and is not intended to provide a comprehensive review of everything that has been done on the subject worldwide during the past two decades. A forthcoming textbook (Hatzor et al., in preparation) will attempt to provide such comprehensive coverage.DDA has been developed by Dr. Gen-hua Shi while he was doing his PhD studies under the supervision of Professor R. E. Goodman at U. C. Berkeley (Shi, 1988). Dr. Shi has invented a new numerical discrete element method which provides a solution for dynamic deformation of block systems, hence its applicability to rock mechanics practice. The method is similar in essence to the finite element method in its implicit formulation of the time integration scheme and where in every time step the minimum potential energy of the entire system is sought, but here every element is a finite block with six degrees of freedom. The blocks are assumed to be stiff (simply deformable) so that most of the energy is consumed by slip along pre-existing discontinuities, the frictional resistance of which is assumed to obey the Coulomb-Mohr failure criterion for rock joints. The greatest advantage of DDA over alternative numerical discrete element methods is its robust area (volume) integration which ensures great accuracy even when the blocks are of irregular shapes, including non-convex blocks which may contain holes. The greatest disadvantage is the necessity to solve in every time step very large matrices of unknowns, imposing great CPU demand when the block system involves a large number of blocks. Another disadvantage is the sensitivity of the solution to the choice of the penalty parameter which is implemented in DDA in the form of stiff springs that are attached to contacts once detected automatically.The inherently dynamic formulation of the DDA method lends itself to solution of dynamic problems in rock mechanics. Dynamic analysis with DDA can be performed in different ways corresponding to different rock mechanics problems and loading conditions. Three main classes of loading conditions which are relevant to rock mechanics applications are discussed here: 1) dynamic loading of a single bock which rests on a stationary foundation, 2) response of a block to dynamic loading of the foundations, 3) wave propagation through a block system.The most common approach is to introduce the dynamic force to a specific block in an otherwise fixed block system and check the resulting deformation, typically the time dependent displacement or rotation of the loaded block. This approach is particularly useful for dynamic rock slope stability studies when a stability of a specific rock block against earthquake vibrations is in question. The first 2D-DDA benchmark test of this approach was performed by Hatzor and Feintuch (2001) who introduced harmonic acceleration functions into a block which rests on an inclined plane. The analytical solution proposed for this problem by Hatzor and Feintuch (2001) was later generalized by Kamai and Hatzor (2008). The first 3D-DDA benchmarking for this approach was presented by Bakun-Mazor et al. (2012) who studied single and double face sliding of blocks which rest on stationary foundations and subjected to harmonic input acceleration functions."