Formulation of discontinuous deformation analysis (DDA) — an implicit discrete element model for block systems

Continuum-based numerical methods have played a leading role in the numerical solution of problems in rock mechanics and engineering geology. However, for fractured rocks, a continuum assumption often leads to difficult parameters to define and over-simplified geometry to be realistic. In such case, discrete representations of fractures and individual blocks must be adopted. In this paper, a newly emerged member in the family of discrete element methods (DEM), the discontinuous deformation analysis (DDA), is presented, including its variational principle, governing equations, solution techniques and contact representation and detection algorithms. Its relative advantages and shortcomings are compared with the explicit distinct element method and the finite element method. An example of the analysis of tunnel stability is provided to demonstrate the capability of this new method.