Modification and Improvement of The DDA Method
Various modifications to the original DDA formulation have been reported in the rock mechanics literature. In the original DDA formulation a first order polynomial displacement function was assumed, so the stresses and strains within a block in the model were constant. This approximation precludes the application of this algorithm to problems with significant stress variations within the block. However, in cases where the displacement inside the block is high and cannot be ignored, the blocks can be divided by mesh. An example of this approach is the research by Chang et al. and also Jing who resolved this problem by adding finite element meshes in the two-dimensional domain of the blocks so that stress variations within the blocks can be allowed.
Higher order DDA method for two-dimensional problems has been developed in both theory and computer codes by researchers like Koo and Chern, Ma et al. and Hsiung. Additionally, Roozbeh Grayeli and Ali Mortazavi implemented finite element mesh based on six node triangular element into the original DDA blocks in order to account for stress variations within the blocks. The DDA contact model which was originally based on penalty method was improved by adopting the Lagrange type approach reported by Lin et al.
Since a blocky system is a high non-linear system due to non-linearity within blocks and between blocks, Chang et al. implemented a material non-linearity model to DDA using strain hardening curves. Ma developed a non-linear contact model for analysis of slope progressive failure including strain softening using the stress and strain curve.
Recent progress in DDA algorithm is reported by Kim et al. and Jing et al. which is a coupling of fluid flow in fractures. The hydro-mechanical coupling across rock fracture surfaces is also taken into account. The program computes water pressure and seepage throughout the rock mass of interest. In its original formulation, a rock bolt was modeled as a line spring connecting two adjacent blocks. Later, Te-Chin Ke suggested an improved bolt model, followed by the rudimentary formulation of lateral constraint of rock bolting.
Moosavi and Grayeli implemented a fully grouted cable bolt element into the DDA algorithm which can be considered another step towards improving the potential of DDA for solving blocky rock masses requiring reinforcements for stability purposes.
Read more about this topic: Discontinuous Deformation Analysis
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